No it doesn't. You can't have a genuine statement of that any more than I can say that it gives possibility for a God which science CAN say anything about. It gives a statement of no value.
Tom Sawyer does not exist. I can prove this using the scientific method, or at least make his existence extremely untenable. Science doesn't always have to be absolute proofs, because it can gather evidence to make a theory more or less tenable, and religion cannot. So, that being said, how does revelation beat this barrier? What does revelation have that makes it immune from inquiry and evidence gathering? I've said that science CAN investigate if there's something to investigate, even if the investigation doesn't make a conclusive statement. "I don't know" is valid, and to say that I don't know about this God of yours hasn't proved that science cannot at all say anything about existence. Science CAN investigate it, it may not be able to give a definite answer though. This problem can change depending on circumstances; Tom Sawyer is easy to render untenable (disprove) because we have a lot of information. Bronze Age myth is easy to render untenable (disprove) too (The pantheon for instance is easy to disprove) stories in the Old Testament are easy to render untenable (disprove). Religion has cowered and now uses sophistry instead of myth to create a God which fits their ability to hide details. The more we learn, the more ground they have given up. At this point trying to equivocate "well it could" is senseless because there's no value in what you suppose here. It's not even religious until you make that spiritual connection. It as IS valid as saying Tom Sawyer could have existed. That doesn't mean he does exist, it doesn't allow you to say you know he exists. At this point Punshhh how could you actually say Science hasn't refuted Religion? Really if we're reduced to using sophism to avoid actually losing the argument here, and that sophism doesn't even have religion at all any more than just trying to make sure Tom Sawyer/FSM/God could possibly exist, even if that existence has in no way any relevance to any religion, why keep taking a few steps away from logic to hold onto it?
Allow me to try a bit of a different tactic, using what you've said. Things we are pretty sure we know. We have a universe, and it wasn't eternally this way, it started with a Big Bang and evidence lends to the theory that a quantum fluctuation occurred that quickly amplified into what we have now, given a vast length of time. That's everything we have. You define a cause to this, and name that cause God, for the purpose of what I'm about to discuss, we'll call this God (A). This God doesn't necessarily have to have ANYTHING else to do except be that quantum fluctuation. Fine.
We'll call this supposed God (B)
You cannot get from what I summed up there (A), to here (B). Not without making something up along the way. (A) Has only one novel function, that being the creation of existence, but then you also propose (B) as if they're the same. There is no necessary reason for this to be so. You might as well have just made up two gods, (A) and (B) and they could have absolutely nothing to do with eachother. But you can't even make (B) valid at all either. There is no line of logic, no reason for (B) to exist, or for (A) to also be (B) (Sorry if this is confusing, it would be nice if I could draw this on a whiteboard...)
(B) is superfluous and untenable. It has no obvious novel function by which we can surmise its existence at all. At least with (A) we have room to consider it, with (B) there is none.
So why suppose (B) at all? Why are you considering it, and why conflate with (A) if you are indeed doing so.
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You know I read that over once...I want to be able to present this idea...but it is screwy in this format...so sorry.