The RNG is seeded by the frame counter when you press start on the title screen.

You can get the same seed every time by holding start and resetting the game. This guarantees that start is pressed it on the first frame of the title screen.

It always yields the same pattern on day 1 as seen in this video:

It seems like the coworkers in Day 2 and beyond also increment the RNG so I haven't found a way to have any other days "solved" like day 1.