This concept is actually pretty cool, you can get creative with how you use the mechanic. I did unfortunately get stuck early into the game, I got one ice cream and then didn't know how to proceed. But for your first game, this is really impressive! I'll give a few quick points of feedback:
Some more contrast between the checkpoint sprite and the background would be nice. It's still visible, but it blends in a bit too much. You could use a lighter color like white for example. Clarity is super important in these types of games!
The tutorial at the beginning was really great for teaching you how to use the mechanic. I think more of that would be good. You could consider starting the game reallyyy slow, to the point where it's almost stupidly trivial. This ensures players aren't getting stuck (like me lol) too early into the game so that they can still have a good experience. Even if it seems too easy, it might actually be the perfect difficulty to start.
You could try to set up checkpoints throughout the game. It's a bit frustrating when you're forced to restart at the very beginning, especially if you've already made good progress. Having to restart those previous sections probably isn't best for this type of game, so having checkpoints would be really useful.
I hope this feedback helps! I really like your idea, so keep working at it! Congrats on submitting for your first game jam!