At least with the latest Python versions (tested on 3.8 and 3.11) this appears to work fine:

• Download the Windows embeddable package you need from the official site, and extract it.

  PS> Invoke-WebRequest -Uri https://www.python.org/ftp/python/3.11.1/python-3.11.1-embed-amd64.zip -OutFile python-3.11.1-embed-amd64.zip
  PS> Expand-Archive .\python-3.11.1-embed-amd64.zip
  PS> cd .\python-3.11.1-embed-amd64
  

• Open the python3xx._pth file corresponding to your version (e.g. python311._pth for Python 3.11), and make sure the following import line is uncommented. This will automatically add site directories used by pip to the Python path:

  # Uncomment to run site.main() automatically
  import site
  

  In Powershell this can be automated by running:

  PS> Add-Content -Path .\python311._pth -Value 'import site'
  

• Download the official pip bootstrap script, e.g. with Powershell:

  PS> Invoke-WebRequest -Uri https://bootstrap.pypa.io/get-pip.py -OutFile get-pip.py
  

• Run the downloaded script (make sure you're using the correct Python executable in the current directory .\):

  PS> .\python.exe get-pip.py
  Collecting pip
    Using cached pip-22.3.1-py3-none-any.whl (2.1 MB)
  Collecting setuptools
    Downloading setuptools-66.0.0-py3-none-any.whl (1.3 MB)
       ---------------------------------------- 1.3/1.3 MB 16.0 MB/s eta 0:00:00
  Collecting wheel
    Using cached wheel-0.38.4-py3-none-any.whl (36 kB)
  Installing collected packages: wheel, setuptools, pip
    WARNING: The script wheel.exe is installed in 'C:\Users\xxxx\Downloads\python-3.11.1-embed-amd64\Scripts' which is not on PATH.
    Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
    WARNING: The scripts pip.exe, pip3.11.exe and pip3.exe are installed in 'C:\Users\xxxx\Downloads\python-3.11.1-embed-amd64\Scripts' which is not on PATH.
    Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
  Successfully installed pip-22.3.1 setuptools-66.0.0 wheel-0.38.4
  

• Run pip from the .\Scripts directory:

  PS> .\Scripts\pip.exe list
  Package    Version
  ---------- -------
  pip        22.3.1
  setuptools 66.0.0
  wheel      0.38.4
  
  PS> .\Scripts\pip.exe install numpy
  Collecting numpy
    Downloading numpy-1.24.1-cp311-cp311-win_amd64.whl (14.8 MB)
       ---------------------------------------- 14.8/14.8 MB 11.9 MB/s eta 0:00:00
  Installing collected packages: numpy
    WARNING: The script f2py.exe is installed in 'C:\Users\xxxx\Downloads\python-3.11.1-embed-amd64\Scripts' which is not on PATH.
    Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
  Successfully installed numpy-1.24.1
  
  PS> .\python.exe -c 'import numpy; print(numpy.__version__)'
  1.24.1
  

how I installed pip into an embeddable python distribution:

1. unpack the python embeddable distro archive and cd there
2. run python ./get-pip.py (got here)
3. EITHER just uncomment string import site inside file pythonXX._pth OR copy folders (at least pip) from the newly-created folder Lib/site-packages/ into pythonXX.zip

now it's possible to python -m pip ...