Does science prove that miracles exist?
I assume you are asking if science can be used to prove that a miracle occurred.
There are two reasons the answer is no. First of all, science has to do with things which are “natural.” In other words, science only deals with events that occur due to the actions of the laws of nature. By definition (at least by the most common definition), a miracle is a supernatural event. Therefore, it is not a “natural” event. This means that, by definition, whether a miracle has occurred or not lies outside of the information realm that science is able to discuss.
Another reason the answer is no is that science can only be used to describe events which are reproducible. An unreproducible event, such as a miracle, is therefore something that the scientific method cannot be used to investigate. Therefore, if a miracle did in fact occur, because miracles are inherently unrepeatable events, science literally cannot study such events.
There is one area in which science can be helpful. Science cannot be used to prove that miracles do happen and it cannot be used to prove that miracles do not happen. Howevver, science say something like this: If such and such thing did in fact happen, then that would be a miracle. For example, if a person was dead for four days (like Lazarus) and was subsequently living (ie. resurrected) then that would be a miracle. This would unambiguously violate natural law, and would therefore be a miracle, by definition. If someone were to, beginning with water only, produce wine, then that would be a miracle. Natural laws, which are what scientists do in fact study, tell us what can happen naturally and what cannot happen naturally. Therefore, although science cannot confirm a miracle and it cannot prove that the miraculous does not happen. However, science could, in principle, show that an event, if confirmed by means other than science, was a miracle.