Cute game.
The flying saucer breaks the game, and I don't see much point in using it, especially for the main game, since you only need the socks to win. The map size is too small for flying to be necessary. You can also clip objects out of the fence quite easily or get out of the map by colliding with big objects like the lock and launching out of the yard. It would be better to have the ability to pause with a key on the keyboard instead of having to click a button on the screen.
The explore mode is fun for a couple of minutes, but there isn't much to do there; it's an empty open zone. Without discovery, exploration loses its purpose and becomes an aimless endeavor.
Unlockable content is nice, but it should not overshadow the main content. Being ambitious is good, but currently, the game lacks focus and doesn't know exactly what it wants to be. Does it want to be a Sandbox with secrets or a Puzzle Adventure?
I wish you good luck in your game dev journey. Good job on submitting the game on time.
Edit: It's probably not a good idea for the player to start under a timer. If they don't know how to play, they will feel pressured to learn fast to avoid losing. A tutorial level might fix this.