As the title suggests, I made this game over the past week and I am looking for some feedback. Still figuring everything out but I think I'm starting to get a good grip of Unity. Please let me know any improvements you think I could make or any mistakes you noticed from me. Thank you for your time!

https://desbytub.itch.io/fossils-of-the-forgotten

It looks and feels great but I don't know these types of puzzles so am locked in level 1. A brief tutorial would really help.

I have played you game and like it very much.
Every aspect is well thought out, with appropriate priorities of minimal development effort for maximum effect -- quite impressive.
Early levels teach the game, making game mechanics understandable without need for additional tutorial.
I have few suggestions in case you want to develop this game beyond the jam:

1. Level progression is good, but I feel that final levels are a bit too easy / straightforward compared to previous ones, maybe you ran out of time when designing them?
2. 'Rewinding' animation could be faster, currently it is a bit tedious to watch the character walk back.
3. Maybe add some reminder of the previous attempt (e.g. as 'ghost' arrows on empty 'program' cells.
4. Previous two points are currently not very important, since the levels are small and short. In case you want to expand the game, some obvious ideas are: allowing to "bump" into a wall during the "programming" phase, various "teleports / flowing currents" to make level topology more complex, etc.

Overall, excellent little game!