I applaud the honesty with which you acknowledge what, exactly, the traditional notion of god would entail relative to the universe that we actually observe. I urge you to read David Hume's work, On Miracles regarding these ideas.
I actually call this conception of god "the video game god."
But consider this: Some supernatural interventions WOULD leave a trace. But we see none. So, insofar as god is the author of the videogame, he has been very careful to make sure that the simulation is, in fact, perfect, and there is no internal evidence of the matrix. This seems very problematic to me: "You must believe in me --- on pain of eternal torment -- but I have taken great pains to cover up any evidence of my existence."
The creationist crowd maintains that such traces *have* been observed. Depends exactly what religion you're looking at, but in Christianity it's stuff like fire falling from the sky, people walking on dry seabeds with walls of water on either side, the virgin birth, people being raised from the dead, the existence of the universe itself, etc.
In discussions like this on science vs. the supernatural I like to refer people to C.S. Lewis'
Miracles, which forms the base for my above arguments.
As for God covering up his existence, God doesn't seem to think he's doing so: According to Romans 1:18-20:
"The wrath of God is being revealed from heaven against all the godlessness and wickedness of men who suppress the truth by their wickedness, since what may be known about God is plain to them, because God has made it plain to them. For since the creation of the world God's invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that men are without excuse."
If you read further on in Romans 1, you see alot of what is popularly thought of as "sin" mentioned, (sexual misbehavior, murder, etc.), but not so much as sins but as punishments for unbelief, in that they are the natural results of unbelief, but God protects people from their own self-destructive inclinations for a while, but stops and lets them do what they want.
It's like a patient going to a doctor with cancer. The doctor investigates the problem and sets up a date to have the tumor removed (or puts together a chemo or radiation therapy regime). In the meantime he treats the symptoms. The date for the surgery comes, but the patient doesn't want to have surgery and cancels. So the doctor goes on treating the symptoms and sets up another surgery date. The patient cancels again. This goes on, and meanwhile the tumor grows and starts spreading to other locations, and eventually the patient runs out of money and the health insurance company runs out of patience. The patient can't pay anymore and the doctor stops treating the symptoms. Not a perfect analogy (there's no money involved in the transaction between God and man), but workable.
Basically, "You must believe in me --on pain of eternal torment-- because I've gone to great pains to make myself obvious. If you ignore the evidence, I won't protect you from yourself."