Think about this, what you wrote. It shows that deep down you perceive of the supernatural as if it should be have naturally. You expect it to be “demonstrated” but that is only meaningful for a mechanistic system that adheres to laws.
This is why so many go astray with atheism, they don’t see how they’ve been trained to only perceive the world as mechanistic, they then want the non-mechanistic to be demonstrable using the mechanistic.
You’re asking the same kind of question as those who seek proof of free will, how can free will be demonstrated? It’s all part of the paradoxical nature of reality.