Such a cool game! It kind of reminded me of Undertale in a way :-D
I randomly stumbled upon the white key the first time I entered the room where it was hidden and naturally went through the white door when I reached it.
Early in my play-through I found the secret room with the time machine, and I got a bit frustrated that I didn't get the chance to return to the rooms after entering through the white door. I think that is a testament to how engaged I got in the game, which is a positive sign!
The only thing I think this could need is a simple description of controls, as I was a bit uncertain if there was something I was missing and didn't know I could do.
I really really enjoyed this game, and is ranked highly among the games I have played at this jam. Good job, and keep at it! :-)