If the game crashes on startup / won't load properly after picking your starter car, try this:

Delete the file with DX12 in

\Origin Games\Need for Speed Unbound\shadercache

and the one in

\Documents\Need For Speed(TM) Unbound\cache

And that should prevent the game from crashing after booting it up and after selecting your starter car. If the issue still persists after deleting both files, try to download the nfs.exe again. Simply delete the .exe, right click the game in your library and repair files.

I am sharing the fix that helped me run the game, it was posted on EA Answers.