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.
I personally believe God as an actual entity as it is presented through religion, does not exist. Or at least not in the way you or I exist. Think of something along the lines of ghost tales or rumored phenomena. The image you conjure up in your head or the lengths people go to to defend themselves against this imagined threat is more powerful than itself as an "entity". So in that vein, I believe that in the way the idea of God itself has shaped civilizations and society as we experience it today is in itself a manifestation of God. So to answer the question, Since God is a concept that has been ingrained for the majority of people living in civilization, no one can truly be "free" from the influence of God. What can be chosen, however is how much God influences your thoughts and actions. In short: Yes, but also no.