Does the very fact that God doesn't ever show himself in a readily available way prove he doesn't exist?

God can't show himself because he is not a physical form. He is a divine consciousness, something that is hard to grasp for us humans because our world is 3D, and that is where your thinking comes from. You must raise your thinking to out of what we know as reality. I know it is hard to grasp, it took me a while too.