In an earlier post I wrote that regarding existence of God, "absence of evidence is not evidence for absence."
This may be true formally but I now think is mistaken in substance. First, complete lack of evidence for "God" would make it impossible to know what the term "God" even meant.
Second, if an arbitrary idea of God were floated (and many very different ones might be), a god that left no evidence of himself in the world is not one I'd bother with heeding in my personal life. As per the previous post, I'd be an "agnostic atheist."
A distinction could be made between knowing that God exists and being able to prove definitively that God exists to another person. One may "know" via some "self-authenticating" mystic communion or private revelation, but be helpless in trying to persuade, i.e., "show," someone who was not a beneficiary of such grace. However, I think that this sort of "faith" could not work at all without a solid foundation in reason.