I actually think God has already done plenty to prove his existence. How everyone interprets that seems to vary (and some don't believe at all).

Maybe this is more about proving something to yourself than about having it proven to you. For example, how do you know your child loves you before they can tell you, or before they really understand what they're telling you?

Personally, from a faith perspective, I think the onus is on me, not on God ("think not what your country can do for you, but what you can do for your country" sort of thing!).