It became known that this game does not work on AMD processors without the support of SSE 4.1. So if you are the owner of such a processor, then unfortunately you can’t fix crashes on startup in Mafia III. However, the developers will likely soon introduce CPU support such as has happened more than one game.
If your processor is suitable for the game and it still crashes, try to remove VCRedist 2015 from the system, then reboot the PC. After that, go to the Redist folder in the game directory and install from there VCRedist 2015.