Write a test program (name it for example glibc-version.c):

Copy#include <stdio.h>
#include <stdlib.h>
#include <gnu/libc-version.h>

int main(int argc, char *argv[]) {
  printf("GNU libc version: %s\n", gnu_get_libc_version());
  exit(EXIT_SUCCESS);
}

and compile it with the gcc-4.4 compiler:

Copygcc-4.4 glibc-version.c -o glibc-version

When you execute ./glibc-version the used glibc version is shown.

the glib source builts the libc6 packages.

https://packages.debian.org/source/bullseye/glibc

$ ldd --version
ldd (GNU libc) 2.39

A system isn't actually limited to one C library. Most, though, primarily use only one, which will also be the one the default compiler uses. And since you're downloading source code to compile, that's the one you're concerned with.

Start with a trivial program:

#include <stdio.h>
int main() {
    printf("Hello, world\n");
    return 0;
}

compile it using the compiler you're going to use for the source code, then use ldd to find out where the C library is:

$ ldd ./libc-test 
        linux-vdso.so.1 (0x00007fff2e5fe000)
        libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007f8c8ad98000)
        /lib64/ld-linux-x86-64.so.2 (0x00007f8c8b171000)

You now have the path to the C library. You could look this up in your package manager to find the package (e.g., dpkg -S /lib/x86_64-linux-gnu/libc.so.6 or rpm -q -f /lib/x86_64-linux-gnu/libc.so.6).

At least in the case of eglibc/glibc, you can run it:

$ /lib/x86_64-linux-gnu/libc.so.6  
GNU C Library (Debian EGLIBC 2.18-4) stable release version 2.18, by Roland McGrath et al.
Copyright (C) 2013 Free Software Foundation, Inc.
⋮

Finally, you could see if you can get clues from objdump -p /lib/x86_64-linux-gnu/libc.so.6, by looking in the version definitions section:

Version definitions:
1 0x01 0x0865f4e6 libc.so.6
2 0x00 0x09691a75 GLIBC_2.2.5
3 0x00 0x09691a76 GLIBC_2.2.6
⋮
21 0x00 0x06969197 GLIBC_2.17
        GLIBC_2.16 
22 0x00 0x06969198 GLIBC_2.18
        GLIBC_2.17 
23 0x00 0x0963cf85 GLIBC_PRIVATE
        GLIBC_2.18 

Note how the GLIBC_2.18 symbol has the most recent version number among the symbols listed, and the library version is indeed 2.18. It's eglibc, though (it aims to be binary-compatible with glibc 2.18, so it uses the same symbol versions).

You could also attempt to use strings to find out something about it. You'll want to specify a longer minimal length (-n), or use grep to search for something:

$ strings  /lib/x86_64-linux-gnu/libc.so.6 | grep 'version [0-9]'
$ strings  /lib/x86_64-linux-gnu/libc.so.6 | grep -iC1 'copyright'

both work for this eglibc.

NOTE: The Debian package utility dpkg-shlibdeps uses objdump under the hood, along with stored symbol information in Debian library packages to determine the minimum versions of dependencies required by binary Debian packages at build time. Basically, it looks at the symbols exported by the binary Debian package, and then finds the minimum versions of the libraries that contain those symbols.