As an example, for those whom are married, do you find it necessary to prove that your wife actually loves you?
Actually, this sort of inductive testing does take place in marriages quite often.
Some of us are just more comfortable to quit trying to prove and examine every single circumstance in life.
Not every single circumstance, no. But the existence or non-existence of God is not your garden-variety circumstance. It's fundamental. Now, my own stance is that one tries to figure matters out. One reasons it through. Some people seem not to believe in "reason." I suppose they think they have reasonable reasons why reason doesn't work--a contradiction by my way of thinking. Reason is the given: we go from there. You can't get "outside" of Reason.
So according to my scheme, there is a 50/50 chance that God exists. Moreover, I've reasoned it out (less certainly) that only one type of God could exist (all-knowing, all-good, etc). I've also reasoned it out that the moral argument against God is invalid (if our morality is subjective, then it can't count as evidence for or against anything, such as the existence or non-existence of God). And so my previous argument that the painful nature of the evolutionary process proves that God doesn't exist fails on those grounds. On the other hand, if God does exist, he is cruel if we grant the truth of evolution--in that if God does exist, that could possibly mean our moral ideas are objective.
That's about as far as I've gotten so far.
"The whole of life goes like this. We seek repose by battling against difficulties, and once they are overcome, repose becomes unbearable because of the boredom it engenders."--Pascal