Most of the steps I took to get this game to run have been taken from Corben78's findings here: https://github.com/ValveSoftware/Proton/issues/530

There seems to be some kind of issue with this game's DRM that makes it crash when killing an enemy during odd days of the month. Either playing the game on an even day of the month or setting the system time to an even day lets the game work. I've tried to run the game with faketime, but to no avail. In addition, I could not run the game in dx11 (HUD would display but the rest of the screen was black) or windowed mode (crash after splash screen), and alt-tabbing would cause a heap of issues, generally ending in the game crashing. To remedy this, I had to use winecfg in the game's prefix ($protontricks 10680 winecfg), enabled wine's virtual desktop at the resolution I intended to play the game at, and unchecked both "Allow window manager to ..." options. I also installed xact ($protontricks 10680 xact).

After all of that, start the game in dx9 mode with proton 4.11-13 and after waiting about 30 seconds, the game should hopefully be running. So far, I've played through the entire marine campaign with no major issues. Be sure to not verify integrity of game cache, as doing so will make the game unplayable, and you will have to copy it from a wine/windows install again.