I'm not mistaken: You have conceded the gist of my case--that there is no rational basis to think God exists. Belief is purely a matter of "faith"--a euphemism for an illogical and unsupported certainty. Your argument, however, gives no reason why anyone should hold that faith. Either one does or doesn't, and there is nothing more to say.
But you don't really believe there is nothing more to say, or we wouldn't be having this discussion. You concede that it would be silly for God to prove his existence through the incarnation, because so few people would be witness to the event. You then go on to insist that God came into the world for a different purpose--to demonstrate his concern. But why isn't that effort equally silly? Whether he was attempting to prove his existence or his concern, this would have been a monumentally ineffectual way to do it. We are supposed to believe that God is not indifferent to us because a handful of scribes tell us so--even though, by your admission, it would be "silly" to believe he exists on that same basis. If there is a string of logic here, it escapes me.
Your explanation of why it is impossible for us to know God except through a leap of faith strikes me as a lame attempt to rationalize his inconvenient absence. So he's immortal; so he's boundless. Why does that prevent him from manifesting himself in some concrete and undeniable way? I didn't think "impossible" was a concept that applied to the Almighty. He created the universe out of nothing--yet he can't make his own existence as obvious as the midday sun? Please.
And if he truly cares for us, then why does he not only refuse to provide plain evidence that we should believe in him but then consign to eternal agony those who are unable to believe without it? A dictator who behaved this way would be regarded as monstrously brutal and unjust. But we are supposed to indulge such eccentricities in him who is supposed to be perfect. That is one of the many "mysteries" that faith is supposed to help us understand and accept. The real mystery is why intelligent people like you put aside all their critical faculties when the subject of God arises.
You seem to have agreed to this debate only to make the argument that there is nothing to debate. If it is all a matter of faith, then those who happen to have faith have reason to believe God exists, while those who do not have faith have none. Faith is belief without evidence, belief without reason. The word that would be used in any other context is not "faith," but "delusion."