So, the game keeps crashing immediately after the load screen/bar when I should be entering the actual game. I have tried playing the game via the GogGalaxy as well as the offline downloader, with the same problem.

Any ideas on how to solve this?

Following. The exact same thing is happening for me.

Which game? There are 9 of them in this series.

I've been having trouble with Might and Magic 7 and 8 myself. And if I run them through GoG Galaxy, it causes Galaxy to act up after the crash and eventually crashes Galaxy if I attempt to re-launch the game.

Might and Magic 6 seems to run fine though.

I can't help with Galaxy; I don't use it. I use the offline installers.

If it is MM8, then my next question would be "Is your save file in Escaton's Palace?". If yes, turn the sound off before loading.

GoG versions do include older Greyface patches, but there are newer patches since 2017.
You can update MM6 thru 8 with the latest Greyface patches, be aware Galaxy could overwrite these should there be updates (not since 2017) or you run a verify or reinstall:
https://grayface.github.io/

You can also try turning off Galaxy's overlay when running these games (or turn off in Galaxy for all games like I do)

Other general old games not working may be this items (definitely make sure DirectPlay and DirectX 9 are done):
Make sure games are NOT installed in any location under Program Files or such.
Make sure the Windows Feature (Legacy) DirextPlay is installed
https://learn.microsoft.com/en-us/answers/questions/1822524/how-to-enable-directplay-on-win-11-xp3-if-i-can-fi
Make sure all DirextX 9.0c files are installed (will not overwrite any DX12 stuff)
https://www.microsoft.com/en-ie/download/details.aspx?id=8109
Make sure all VisualC runtime versions/bitness are installed
https://www.techpowerup.com/download/visual-c-redistributable-runtime-package-all-in-one/