Okay, I might be open to the theoretical possibility, but what kinds of evidence could there be that miracles are actually possible?

Well, the thing about miracles is that they are rare and unique by definition. Also, they are exceptions to the laws of nature, so they're not reproducible or testable in the scientific sense.

But if the claim is that a strange event still happened at such and such place and such and such time, in other words, at a point in history, then there needs to be good historical evidence that holds up to scrutiny by the methods of historians, which cannot be simply repeated in a test-tube in a lab. That's called historiography. And that's what need to do with any event, including a report of an event that seems strange or inexplicable, such as a miracle.

Perhaps the best example of a miraculous event with well-attested historical evidence is the resurrection of Jesus. So to answer your question – the kind of evidence that we need to look into for a miraculous event is historical evidence.