OK - I think I can concede that. But with that argument, Descartes only proved that he existed because he was a thinker. Ergo, only thinking things can prove they exist that way. But, fortunateley, it's not just thinking that proves existence, being red proves the existence of red objects, being dead proves the existence of dead things, being a scold proves the existence of my wife, and so on ad infinitum.
But we aren't actually concerned with existence, are we? We've sidetracked ourselves: what we want to find out is how things came to be in the first place.
Religions hold that there was a Prime Mover and He was the uncaused cause. He was also the creator of all things, so if a thing exists - which plainly, many things do - He created them. Cogito has nothing to say about this (so far as I am aware). Religions believe this to be so, and hope one day their beliefs will be demonstrated to be true
Your scientific hypothesis says that there must be a natural law of physiscs that says something can spontaneously come into existence, but we don't know what it is yet. But there is hope that we will know one day.
Where's the difference?
Who cares what happened at any time after the Big Bang? God was there before it. Every one of your scientific laws can easily co-exist with the Supernatural Being who created them, along with everything else. It is hard to see how they can exist at all without a Supernatural Being.
I won't dispute your distinctions.
It is religious dogma that Yaweh(for example) is perfect, and that leads to inconsistencies that make faith look ridiculous. Why are you assuming God is bound to perfection? Why does He have to be? Why can't He learn like the rest of us, and make mistakes in the process?
And I would also submit that our understanding of religion and what we believe in has advanced, just as scientific theory has: from fear of thunderclaps to more sophistcated understandings of who we are and why we are here. Out of Zoroastrianism grew Judaism, then Christianity and then Islam; before Zoroastrianism, pagan beliefs, myths and superstition, perhaps, but all leading to the Ultimate Truth.
I believe they are theories which give (partial) explantions for our current hypotheses. I agree that these theories are constantly being refined in the hope that we will eventually have a Unifed Theory that explains everything ... or at least, as Hawkins put it, enables us to know the mind of God.