I believe that God is supernatural in the sense that He is and can operate outside the physical, material universe. But I also believe that He can manifest Himself in the physical world. Either physically by direct intervention or by displays of His power. I think that what we call miracles is evidence of that. Now the problem with that is that while many miracles are documented, catching one while it's happening to record it and analyze it is a different matter. I don't know of any that have been caught in the act.
So be a Mythbuster and come up with a plan to test for God. Be inventive. It might be a hard task, but if you succeeded, just think of the witness for God you will be.