I have a working theory that I'm chewing on, but it's not objectively provable. Obviously, to pose your question, you must assume that God exists for the sake of the argument. If so, the next question is, why would an originator create our universe in the first place? It's reasonable to say that intelligent people only do something if there is a reason. My line of thought assumes the same rationale applies to an intelligent originator of all things, meaning that we also exist for a reason.
This could be very wrong, and I know I'm talking with an atheist, but in consideration of the non-intervening god scenario you mention, maybe the originator is hands-off intentionally, so he doesn't steer our development and interfere with our free will choice. Maybe we are living an IQ test and a test of allegiance.
The test may be, "Are we smart enough to know that everything doesn't come from nothing, which breaks the objective rules of our material universe and hints at a first cause argument that we both have no proof of? Secondly, would we align ourselves with that originator, trusting his reasons for creating us? This leads me to the stand-offish God idea.
I used to believe God was personal because that's what the Church taught. But that seemed weird, and you can only be so intimate with someone you never see and can never have a good chat with over coffee. To me, personal means intimate, two-way conversation and time spent physically together.
I am with you that there is no direct evidence of God, but I allow for what I don't yet know, as any good scientist, theist, or philosopher should. Beyond the Big Bang singularity, our very existence might be the best clue of an originator if one has the imagination to explore that. Or, like you say, maybe another possibility will tie up the loose ends.