This seems to me to be at the core of the original question. If something seems more optimized than a current generally accepted description of the (not really random, but more to the point, natural) processes, then we have to take a deeper look at the “natural processes” we assumede, and think about whether there is some other influencing factor we didn’t consider.
The bottom line theological point is this. I do believe that God exists, and that God created this universe in which we live. I also believe that God knew what She (note that God is not male or female, any Male Chauvinistic Pigs out there; that is my only reason for using the less common female word) was doing when He created this universe - from a physicist’s viewpoint, including the time and space dimensions that we feel as we live here. If God wanted us to know for certain that He does exist, He would have easily left such a clear signature that it would be obvious, even to us humans. So anyone who tries to prove that God exists by examining evidence is wasting his or her time, since that is not something that God wants us to know for sure - along with a lot of other things. God did not tell each of us exactly what is straight from Him, or what is some human’s interpretation of what that person thinks God said. Here again, God put us into an uncertain world, expects us to deal with the uncertainty that we face, and learn from our experiences in this world, where we do get to experience things that we will not experience in Heaven.
So, No, oddXian, you do not have a method for proving the existence of God. If there is something that seems more optimized than our current expectations, we can easily develop different natural explanations that give the observed results.
And, No, Adamjedgar, God did not give us an absolute source of truth, that we can explicitly understand exactly what God wants us to do, and consider everyone who doesn’t understand what we “know” to be the truth in exactly the same way we do, is wrong. There are many steps in your assumption that you have a perfect source of what God wanted to say to you in the bible. The first is really insurmountable: God has chosen to put us into a world where we cannot even prove that God exists. Thus, there is no way that anyone can prove that any written thing absolutely came from God. I do personally believe that the bible was inspired by God, but that is a belief, not a statement of fact, no matter how much I do not want to even think about the possibility that I might be believing something that is not 100% true. And then there are all the other aspects of interpreting the bible, many of which St. Roymond has pointed out. And the question of what is scripture, and what is not.
My conclusion is that God does not want me to prove anything, just to witness to what I believe and why, and maybe that will help someone else have a better relationship with Him.