The epistemology demanded by science is therefore a falliblistic view of knowing. The basis for this lies in testing. A scientific explanation must be open to any competent investigator to test and evaluate. Revelatory experiences are not universally open to all, and intuitions about the universe are wildly different for different people and cultures, so non-naturalistic explanations are ruled out of the domain of science. A useful way to approach this is to ask what a non-naturalistic explanation would look like.
Explanations are equations, of a kind.
If a non-natural explanation is to work, it has to put something that is neither empty nor circular on the other side of the equation. Something is non-natural if it isn't natural' is entirely empty until we know how to distinguish between the two. We can distinguish between our present ignorance and something that's in-principle not scientifically explicable, surely. We could obviously not use empirical observations - they depend on the ordinary course of physical processes. The answer is, nothing.