Why is a conserved quantity under a certain transformation the generator of that transformation?

Question

I would like to know if there is any explanation at the level of a first introdutory course in quantum mechanics of the fact that if we have a conserved quantity under a certain transformation, then that quantity is the generator of that transformation. For example we can prove using Noether's theorem that the momentum is conserved under a spatial translation. But why does it imply that the momentum operator is the generator of the translation transformation? I would like to stress the fact that I'm looking for an undergraduate level explanation, if there's any, like of an introductory course to quantum mechanics.