With any 387.* driver (387.22, 387.34) Talos Principle hangs during loading with my GeForce GTX 970 (occasionally it seems to load fine with 32bit binary, hard to find a pattern). Following error is always showing in dmesg afterwards:
NVRM: Xid (PCI:0000:01:00): 32, Channel ID 00000033 intr 00040000
I am not able to reproduce that Xid, I will keep trying.
Are you running the build 326589 of the game (top-right corner in the main menu)?
The game was recently updated to fix a swapchain re-creation issue, which I think is what fixed your initial bug rather than updating to 390.25. But it could be a different bug.