I'm not here to prove anything and maybe God is not either. You assume that if a God exists that he would want everyone to know of his existance and would be interested in proving it to them. Maybe he does not.
Any god who requires humans to follow specific tenets of religion, under the threat of eternal punishment if they do not, rightfully should
make himself and his intentions clearly known. Otherwise, he's just being an unreasonable jerk. As always, I would allow for the possibility of a "hands off" creator, but such an entity would not give a flip about dogma, and considering you made this statement earlier:
In the case of religion you are wagering your life on it.
you are clearly not a deist. So yes, I would expect your presumably just and benevolent god to be very concerned with demonstrating his existence.