This answer is summarized below.

• MBR partition a 16 GB or larger flash drive to contain a FAT32 volume and an ExFAT volume.
• Copy all the files, except sources/install.wim, from the mounted Windows ISO file to the FAT32 volume on the flash drive.
• Copy sources/install.wim from the mounted Windows ISO file to the ExFAT volume on the flash drive.
• Boot from the flash drive and enter a command to split the install.wim on the ExFAT volume to two files placed on the FAT32 volume.
• The result is an USB flash drive which can be used to install Windows 11.

The steps are given next.

1. Goto Microsoft's Download Windows 11 website and download the Windows 11 disk image (ISO) for x64 devices. In my case, the Win11_24H2_English_x64.iso file was downloaded to my Downloads folder. If your file name is different, then make the appropriate substitutions when entering the commands below.

   Insert a 16 GB or larger flash drive in an USB port on or connected to the Mac.

2. Open a Terminal application window.

   Use the command below to determine the identifier for the USB flash drive. I my case, this was disk2. If your identifier is different, the make the appropriate substitutions in the following commands.

   diskutil list external
   

   Enter the command below to format the flash drive.

   diskutil partitiondisk disk2 mbr fat32 MYFAT32 8G exfat MyExFAT R
   

   Enter the command below to remove all extended attributes from the Windows ISO file. This will remove the quarantine placed on the file when it was downloaded.

   xattr -c ~/Downloads/Win11_24H2_English_x64.iso
   

   Enter the command below to mount the Windows 11 ISO file. In my case, the output from the command shows the file was mounted on /Volumes/CCCOMA_X64FRE_EN-US_DV9. If your folder name is different, then make the appropriate substitutions when entering the commands below.

   hdiutil attach ~/Downloads/Win11_24H2_English_x64.iso
   

   Enter the command below to change the current directory to /Volumes/CCCOMA_X64FRE_EN-US_DV9.

   cd /Volumes/CCCOMA_X64FRE_EN-US_DV9
   

   Enter the commands below to copy the files from the mounted ISO to the flash drive. Note: Since the install.wim file is very large, the cp command can take a while to complete.

   rsync -r -t --exclude=sources/install.wim . /Volumes/MYFAT32
   cp sources/install.wim /Volumes/MyExFAT
   

   Enter the commands below to unmount the Windows 11 ISO file.

   cd ~
   hdiutil detach /Volumes/CCCOMA_X64FRE_EN-US_DV9 
   

   Enter the command below to eject the flash drive. Afterwards, you can remove the flash drive.

   diskutil eject disk2
   

   You can quit the Terminal application.

3. Using the computer where Windows is to be installed, UEFI boot from the flash drive. You should get a window similar to the one shown below. You can ignore the contents of this window.

   

4. Press the shift+F10 key combination to open Command Prompt window.

   Enter the command below. From the output, determine the drive letters for the MYFAT32 and MyExFAT volumes. In my case, the was C and D respectively. If your letters are different, the make the appropriate substitutions for c:\ and d:\ when entering the dism command given below.

   echo list volume | diskpart
   

   Enter the command below to create the install.swm and install2.swm files in the c:\sources folder. Note: This command will take a while to complete.

   dism /split-image /imagefile:d:\install.wim /swmfile:c:\sources\install.swm /filesize:4000
   

   Enter the command below to close the Command Prompt window.

   exit
   

5. Close the window. When the popup shown below appears, select "Yes". The computer will reboot.

   

   The next time you UEFI boot from this USB flash drive, you should encounter the following window. You then can proceed and install Windows 11.

   

Example of Using the Terminal Window

Last login: Sun Mar  9 09:16:57 on console
davidanderson@Davids-Mac ~ % diskutil list external
/dev/disk2 (external, physical):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     FDisk_partition_scheme                        *15.9 GB    disk2
   1:                 DOS_FAT_32 ⁨MYFLASHDRV⁩              15.9 GB    disk2s1

davidanderson@Davids-Mac ~ % diskutil partitiondisk disk2 mbr fat32 MYFAT32 8G exfat MyExFAT R
Started partitioning on disk2
Unmounting disk
Creating the partition map
Waiting for partitions to activate
Formatting disk2s1 as MS-DOS (FAT32) with name MYFAT32
512 bytes per physical sector
/dev/rdisk2s1: 15594504 sectors in 1949313 FAT32 clusters (4096 bytes/cluster)
bps=512 spc=8 res=32 nft=2 mid=0xf8 spt=32 hds=255 hid=2048 drv=0x80 bsec=15625000 bspf=15230 rdcl=2 infs=1 bkbs=6
Mounting disk
Formatting disk2s2 as ExFAT with name MyExFAT
Volume name      : MyExFAT
Partition offset : 15628288 sectors (8001683456 bytes)
Volume size      : 15370240 sectors (7869562880 bytes)
Bytes per sector : 512
Bytes per cluster: 32768
FAT offset       : 2048 sectors (1048576 bytes)
# FAT sectors    : 2048
Number of FATs   : 1
Cluster offset   : 4096 sectors (2097152 bytes)
# Clusters       : 240096
Volume Serial #  : 67cdc143
Bitmap start     : 2
Bitmap file size : 30012
Upcase start     : 3
Upcase file size : 5836
Root start       : 4
Mounting disk
Finished partitioning on disk2
davidanderson@Davids-Mac ~ % xattr -c ~/Downloads/Win11_24H2_English_x64.iso
davidanderson@Davids-Mac ~ % hdiutil attach ~/Downloads/Win11_24H2_English_x64.iso
/dev/disk3                                              /Volumes/CCCOMA_X64FRE_EN-US_DV9
davidanderson@Davids-Mac ~ % cd /Volumes/CCCOMA_X64FRE_EN-US_DV9 
davidanderson@Davids-Mac CCCOMA_X64FRE_EN-US_DV9 % rsync -r -t --exclude=sources/install.wim . /Volumes/MYFAT32
davidanderson@Davids-Mac CCCOMA_X64FRE_EN-US_DV9 % cp sources/install.wim /Volumes/MyExFAT
davidanderson@Davids-Mac CCCOMA_X64FRE_EN-US_DV9 % cd ~
davidanderson@Davids-Mac ~ % hdiutil detach /Volumes/CCCOMA_X64FRE_EN-US_DV9
"disk3" ejected.
davidanderson@Davids-Mac ~ % diskutil eject disk2
Disk disk2 ejected
davidanderson@Davids-Mac ~ % 

Example of Using the Command Prompt Window

Microsoft Windows [Version 10.0.26100.1742]
(c) Microsoft Corporation. All rights reserved.

X:\sources>echo list volume | diskpart

Microsoft DiskPart version 10.0.26100.1150

Copyright (C) Microsoft Corporation.
On computer: MININT-NBNQP5I

DISKPART>
  Volume ###  Ltr  Label        Fs     Type        Size     Status     Info
  ----------  ---  -----------  -----  ----------  -------  ---------  --------
  Volume 0     E                       DVD-ROM         0 B  No Media
  Volume 1     C   MYFAT32      FAT32  Removable   7629 MB  Healthy
  Volume 2     D   MyExFAT      exFAT  Removable   7505 MB  Healthy

DISKPART>
X:\sources>dism /split-image /imagefile:d:\install.wim /swmfile:c:\sources\install.swm /filesize=4000

Deployment Image Servicing and Management tool
Version: 10.0.26100.1150

The operation completed successfully.

X:\sources>exit

According to the first answer here, https://superuser.com/questions/383235/create-a-bootable-usb-drive-from-a-dmg-file-on-windows, there's a tool with a free trial called TransMac that can do it. Just make sure the USB drive is formatted with GPT and not MBR.

What might be easier, however, is that that model has support for Internet Recovery. If you boot holding Command-R and you have a WiFi connection, it can actually boot into recovery mode without a recovery partition on a drive (or even without a working drive).

Having said that, your description of a crash right after the boot chime could signify a more serious hardware problem and you may not be able to boot anything. If you boot holding the option key down, the startup disk selection screen should appear. If it crashes anyways, you may be looking at a hardware problem.

Use TransMac, which has a 15-day trial period and works flawlessly.

1. In the left pane, right click the USB Drive and select Format Disk for Mac

2. In the left pane, right click the USB Drive and select Restore with Disk Image

3. Point to your .dmg (or choose All Files to select an .iso) file and click Open.

It will take a few minutes depending on size of .dmg and speed of USB drive, but once done you can pop it into your mac, hold down the option key when turning on the mac and choose the USB drive.

OK. Here are some instructions from Gizmodo that will put the ISO onto the flash drive with a Mac... they won't make it bootable though... read on...

1. Open a Terminal (under Utilities)

2. Run diskutil list and determine the device node assigned to your flash media (e.g., /dev/disk2)

3. Run diskutil unmountDisk /dev/diskN (replace N with the disk number from the last command; in the previous example, N would be 2)

4. Execute sudo dd if=/path/to/downloaded.iso of=/dev/diskN bs=1m (replace /path/to/downloaded.iso with the path where the image file is located; for example, ./windows7.iso)

5. Run diskutil eject /dev/diskN, and remove your flash media when the command completes (this can take a few hours on slower drives)

Now... after you read all that, on the Gizmodo page it says that if you want to make it bootable you should use a utility called Live USB helper they link to (which isn't there any more) and use a Mac mounting tool (which isn't there either!) to force the ISO to mount on the Mac so you can copy the files over. So... that article may prove useful, but probably not. I can find other copies of Live USB helper out there, but they are all Windows executables.

One method that will work is to swap the hard drive out of the PC and into the Mac. Put your Windows 7 installation disc into the Mac optical drive, and install Windows 7 on that drive. Once it is up and running (don't worry about drivers yet), follow these steps.

1. Run Command Prompt as administrator
2. Type to Command Prompt: %windir%\System32\Sysprep\Sysprep.exe, and hit Enter
3. In sysprep dialog that opens, choose “System Cleanup Action” as “Enter System Out-of-Box-Experience (OOBE)”, select “Generalize”, and select “Shutdown Options” as “Shutdown”. Click “OK”
4. Sysprep generalizes now your Windows 7 setup and shuts down your computer. Do not run any other programs during this phase!
5. Remove the drive from your Mac. Put it back into the PC.
6. Boot the PC from sysprep generalized hard disk. You will notice Windows booting as if it was the first boot after installation, installing default and updating registry. One or two reboots are needed, depending on your system specifications
7. When Windows finally boots up, you will need to enter all information as if this really was a new, fresh installation

All that is from here, but it applies in this situation a well, since you would be moving a Windows 7 installation from one computer to another. Considering that trying to make a Windows bootable USB stick with a Mac requires tools that either don't exist any more or are not being developed any more... this second method will most likely prove more dependable.

Note: Links to instructions for other versions of OS X/macOS can found here.

User Josué Mpindi posted a question, where this answer was confirmed to work for macOS Sierra in a comment. Note that where necessary, you would need to substitute Sierra references for El Capitan in the instructions.

Note: A version of this answer, which uses macOS to create the USB flash drive OS X El Capitan installer, can be found here.

Using Windows to create an USB flash drive OS X El Capitan installer requires third party software beyond just TransMac. The steps below outline one possible method for creating an USB flash drive OS X El Capitan installer using Windows and other free third party tools.

Note: These instructions will not work for Yosemite. For the correct Yosemite instructions, see this answer.

1. Use Microsoft Edge (or some other web browser) to download the following installers to your Downloads folder. The file names are current as of September 22, 2022. If both 32 bit and 64 bit versions are available, the 64 bit version is given in the table.

   Product	Use	Installer	Type
   El Capitan 10.11†	Free for use on Mac computers	InstallMacOSX.dmg	Mac Disk Image
   7-Zip	Free	7z2201-x64.exe	Application
   TransMac	15 day free trial	tmsetup.zip	Compressed (zipped) Folder
   Paragon Partition Manager Community Edition 64bit	Free for personal and home use	Paragon-1081-FRU_WinInstallDemo_x64_17.9.1_000.exe	Application

   ^†If you get the message “InstallMacOSX.dmg can't be download securely”, then select “Keep”, as shown below.

   

2. Install all downloads except “El Capitan 10.11”. If you wish, the installed downloads can be uninstalled from the Windows Control Panel after use.

3. Use a 7-Zip File Manager application window to extract the OS X Install ESD folder and the InstallAssistant.icns file to your Downloads folder. From a File Explorer window, start by navigating to your Downloads folder. In this window, right click on the InstallMacOSX.dmg Mac disk image file, then select "7-Zip" > "Open archive". This should open a 7-Zip File Manager application window. In this window, right click on each file or folder in the order given in the table below, then select the corresponding action. When finished, close the 7-Zip File Manager application window.

   File or Folder	Action	Type	Comment
   Install OS X	Open	Folder
   InstallMacOSX.pkg	Open Inside *	Package File
   InstallMacOSX.pkg	Open	Folder
   InstallESD.dmg	Open	Mac Disk Image File
   OS X Install ESD	Copy To…	Folder	See footnote ‡
   OS X Install ESD	Open	Folder
   BaseSystem.dmg	Open	Mac Disk Image File
   OS X Base System	Open	Folder
   Install OS X El Capitan.app	Open	Folder
   Contents	Open	Folder
   Resources	Open	Folder
   InstallAssistant.icns	Copy To…	Apple Icon Image File	See footnote ‡

   ^‡The destination should be your Downloads folder. If this Downloads folder exists on a volume that is not NTFS formatted, then see this answer.

4. Insert a 16 GB or larger flash drive into an USB port. If prompted, you do not need to initialize the flash drive.

5. Open the TransMac application with Administrator privileges. (In other words, right click on the TransMac icon, then choose "Run as administrator" or "More" > "Run as administrator".) In the TranMac application window, take the following actions.

   • Select "Tools" > "Settings" from the pulldown menu. In the "General" tab of the "Settings" popup, select the same copy options as shown below.

     

     Select OK when finished.

   • Right click on the USB flash drive icon in the treeview pane, then select "Restore with Disk Image". In the "Restore Disk Image to Drive" popup , choose to "Open" the OS X Install ESD\BaseSystem.dmg Mac disk image file in your Downloads folder as the Disk Image to restore, then select the OK button. Next, select Yes in the "Last Warning!" popup.

6. Open the Paragon Partition Manager 17 CE application. Select to resize the partition with the Apple HFS volume on the USB flash drive to maximum size, as shown below. Next, select the "Change now" button. When finished, select the "Close" button.

   

   Next, select to change the volume label on this Apple HFS volume from "OS X Base System" to "Install El Capitan", as shown below. Next, select the "Change now" button. When finished, select the "Close" button.

   

   When finished, close the Paragon Partition Manager 17 CE application window.

7. In the existing TranMac window, take the following actions.

   • Select "Tools" > "Refresh Drive List" from the pulldown menu.

   • Navigate to root folder on the USB flash drive volume labeled Install El Capitan, as shown below.

     

   • In the listview pane, right click, then select "Copy Here", as shown below.

     

     Select to copy the OS X Install ESD\BaseSystem.chunklist and OS X Install ESD\BaseSystem.dmg files in your Downloads folder. Repeat to copy the InstallAssistant.icns file in your Downloads folder.

   • In the listview pane, right click on the InstallAssistant.icns file, then select "Rename". Change the name to .VolumeIcon.icns. When finished, the treeview and listview panes should appear as shown below.

     

   • Navigate to System\Installation folder on the USB flash drive labeled Install El Capitan, as shown below.

     

   • In the listview pane, right click on the Packages file, then select "Delete". When prompted, select the Yes button in the popup to confirm.

   • In the listview pane, right click, then select "Copy Here", as shown below.

     

     Select to copy the OS X Install ESD\Packages folder in your Downloads folder. (This may take a while to complete.) When finished, the treeview and listview panes should appear as shown below.

     

   • Close the TransMac window.

8. Use the File Explorer to delete the OS X Install ESD folder and InstallAssistant.icns file in your Downloads folder. If you wish, you can also delete the downloaded files. When finished, close the File Explorer window, then empty the Recycle Bin.

References

• How do I create El Capitan installer on a Catalina (or post-El Capitan) installed Mac for use on USB boot installer?
• TransMac Help
• Paragon Hard Disk Manager Version 17 User Manual
• Apple Disk Image Utilities
• HFSExplorer
• DMGExtractor
• dmg2img
• HFS+ for Windows
• Tar and Curl Come to Windows
• dd for Windows
• SuperDuper
• HOW TO QUICKLY CREATE A MACOS BOOTABLE USB ON WINDOWS 10