This is Russell's teapot. You can not prove that infinite states do not exist. In fact, common models of physics assume possibility of infinite number of states

This is Russell's teapot. You can not prove that infinite states do not exist. In fact, common models of physics assume possibility of infinite number of states by depending on formalism axiomatically assuming infinite sets (e.g. axiom of infinity in Zermelo–Fraenkel set theory).