Ding, you touch upon a few good points:
God is the perfect willing mentor to the sincere student wishing to find his way on the path. The key here is the genuine wish to learn and to exceed the self.
God is known only through direct inward experience spoken to the soul.
God is an inward experience so AFAIK, cannot be proven or shown outwardly to a skeptic without harm except through yogic means, and then, only when done without self.
God is found in the spiritual heart (4th thru 7th chakras) by His advent, through a sincere (selfless) inner desire to know something greater and higher than oneself, so will never be found or proven to the ego-driven skeptic standing on one foot daring him to make himself known through the doubting, skeptical mind, as much as I know that just sounds like a cop out.
That's just the way it is and is the same regardless of faith because all faiths lead to the same place. It is the cosmic safety valve which keeps out people not yet ready to advance within the spirit, which would only cause them to fall lower instead, which is a grave offense.
Which of course all of this is always taken as just a cop out by the doubting, ego-driven individual! But that is just how it is. Much like the lions at the gate. Part of the mechanism of keeping out people unless and until they are truly ready to move past the physical and leave the material effulgence.
So now of course go right ahead and doubt me!