I'm having similar problems, and it's happening so often I either save every 5-10 minutes or risk losing 20-40 minutes of progress to a crash.
I'm running an Asus ROG Strix B650-F with a Ryzen 9 7900X with 32 gb of ram and an Nvidia 3070. Game is installed on C which is an nvme drive with plenty of free space. My husband has the same set up except he's running a 4080 and had crashes early on but they appear to have gone away for him almost entirely.
Tried a number of solutions I saw online. Tried turning off V Sync, tried limiting framerate to 60, tried running in admin (that caused immediate crashes) tried running vulkan (5 minute or less crashes) tried running directly from the game instead of via the launcher (not much of an improvement). It crashes in multiplayer harder than in single player, taking down my entire machine. Error reports always seem to point to driver or DX issues or whatever.
I desperately want to play this game, I'm watching all my friends get massively far ahead cause they're not constantly interrupted and set back. At this point it's so much more frustrating than it's worth, I don't know that I'll bother continuing to try.
I really hope they fix things, cause right now I feel like I'm not just missing out on an otherwise phenomenal game, but also on any real chance to play with my friends at all.