But I've a different approach to counter your POV here; lets assume-- if the proof is purely private, it lacks normative power. It cannot be used to establish truth because it provides no way to distinguish between a divine intervention and a neurological event.
Many has experienced God in many forms and levels of consciousness. So why to limit ourself to physical or mental "proofs". The only permanent reality in our life is the soul. So let's start there/with this.