How can symmetry holding for a system have a consequence of conserved quantity or vice versa, in an intuitive way?

Question

does symmetry leads to conserved quantities or conserved quantities leads to symmetry for the given system? which among the statement is more fundamental? and what makes that fundamental (intuition)? i don't need any answer just saying its a Noether's theorem but rather i need some greater explanation for why it happens like that with an deeper intuition.