Atheists, if God existed what would you expect God to do to prove that He exists? What would be adequate proof for you to believe that God exists? Would you expect absolute proof of would you accept evidence?
To try to answer to this, we could compare to methods of providing evidence for various other things/objects/ideas.
So, if it were a dog, for example - we could ask to see photos of the dog, and if we couldn't get those, then ask if we could be taken to the dog to verify its existence ourselves. Less convincing, but still evidence, would be hair from the dog, a DNA analysis of the dog, a license obtained for the dog, evidencing the dog's mother or father, footprints the dog has left on your property. If we could approach God, point to where He lives, see His "tool marks" within His "creation" - and then verify that those are exactly what those things are claimed to be (that the category "God" is appropriate to describe this being, or that the "tool marks" are most definitely from this category of being) then that would be a start.
Now, considering your point that God may not exist "within the material world" - well, we can also look at the evidence we have for things that make no material presentation in reality. For example, "thought" itself. There is no material one can point to that represents a human thought - and yet, with our mutual understanding of the concept layed down as the base, we can readily and easily see the results of human thought all around us, and indeed, we get evidence handed to us at all times from ourselves and any other human being around us who ever say anything original (freshly formed in this case) at any time. We have almost no choice but to accept these things as products of human thought because we have ongoing firsthand knowledge and experience with our own thoughts. God, however, has exactly the same presentation and
non-ongoing evidence as any mythical creature that has ever had a story written about it. And unfortunately, that is simply not convincing. And if God does not present in the material realm, then the evidence can
NEVER be firsthand like in the above paragraph about the dog! When the idea that God does not present in the realm of the material is assumed, then even a mythical creature is more likely to be found than God is in our world!