Interestingly, I was reading a "brief history of time" by Stephen Hawking a few years ago, and one of the more interesting points I found was when he was discussing his "proof" of the big-bang theory (his doctoral work). The problem was that as you said earlier everything after the big-bang followed scientific/natural patterns, but in order for the big bang to occur all the laws of physics had to be broken, thus "proving" the existence of God. According to Hawking the Catholic church immediately adopted his information. At the time of the book writing, Hawking was trying to DISPROVE his own proof of the Big Bang, because it resulted in a singularity.
Also, a clear point is that no matter what evidence one can find, there can be no disproof of God, because the very nature of omnipotence is that even if you can scientifically prove that everything has followed a natural sequence of events, you cannot prove that the natural sequence was created by God.
My quabble with "science" is that no matter what the evidence it is a predetermined assumption that there is no God so any evidence that points toward a God is automatically rejected in search of something else. For instance Hawking working to disprove his own work because it indicated the work of an omnipotent being. I can understand the purpose of science is to investigate all possibilities, but if there is even *some* evidence for God (or the flying spaghetti monster or anything) then it should remain on the table as an option?