Hien B. answered 03/19/19
Top Philosophy Tutor w/ Master's degree from Oxford
Strictly speaking, you could never absolutely prove that Santa Claus doesn't exist. You could know that Santa Claus doesn't exist, as long as he actually doesn't exist and knowledge doesn't require absolute certainty (I don't think it does). In terms of what you can be absolutely certain of, at most you can say that we can be certain that Santa Claus probably doesn't exist, or that we are justified in believing that Santa Claus doesn't exist.
So, I think this is only an epistemic problem if one believes that knowledge requires absolute certainty. For if it doesn't we can still say that we could know that Santa Claus doesn't exist. But if it does require absolute certainty, then perhaps this is a problem since it turns out we wouldn't know what we think know (that Santa Claus doesn't exist). Whether knowledge requires absolute certainty, however, is a separate debate.