[immibis]

Symmetries produce conservation laws if you accept and understand Lagrangian mechanics. That's a big asterisk IMO especially if you've never heard of Lagrangian mechanics and then you try to understand Noether's theorem.

Doesn't getting from Newton to Lagrange already rely on the existence of conservation laws? Apparently if we take Lagrange as fundamental, then it works, and a variation of it works in quantum mechanics, so it does seem to be fundamental, but if you're trying to get from Newton's laws to Noether's theorem, you can't get from here to there without fully grasping Lagrange first.