Caedes
there can never be empirical proof of the supernatural by definition. Is your god limited in his powers?
My definiton of supernatural is something not explained by our current understanding of the laws of physics, cosmology, or natural selection.
A god that DID pre-exist this Universe and that WAS independent of our space-time and that DID not have an origin would be able to prove itself and would be as supernatural. Of course, no such god has ever proved itself, hiding behind ineffability (Shaman talk for "can't answer that").
I have no problem with assigning your god the same probability of existence as a celestial tea-cup.
Ah, but what if I believe in the IDEA of 'god'? Maybe that 'god' is what 'connects' people? That is is nothing other than a consequence of sentient being aware of themselves and will have developed as an idea wherever creatures become sentient and realise that there are shadows... everywhere... and that you can't see what is in shadows but if you're a thinking creature you can IMAGINE it.
Such a defuse entity is not even an entity, it is a force, and it might not even be a measurable one outside of the mind of those that see things that way. God as a paradigm.
But as it's only possible proof is in the thoughts of the person holding such a belief, unless the person holdin such a belief is lying about having such a belief, then they have a personally provable god that is not supernatural, as the only proof required is thought. Cogito ergo theos summae - "I think therefore god is" (I think, my Latin is dreadful).
Of course, they cannot prove it to others but as the only proof needed for another person is the acceptence that someone could indeed have such an idea, a god of that description is far more provable than the normal gamut of re-hashed stone age monster skymen or modernistic illustrations of the unprovability of such old-fashioned ideas.
It's like the idea of a soul. I think this is based on dreaming. A soul is a pretty reasonable supposition to explain dreaming to early man. Therefore any sentient ctreatures that have evolved and experience any state like dreaming will have developed a similar idea to explain it.
We are the story tellers. Dolphins and chimps might be smart, but I'm not convinced they are story tellers. And having developed the ability to tell stories (probably because it wooed the ladies), and developed it (as those with the gift of the gab got laid more often), it is natural we came up with stories to explain things... even if they didn't need explaining.
Ideas of god and souls are natural concequences of creative story telling and dreams. They evolved with us. As they were never ever really anything other than ideas, of course they exist.