(Warning, Boring intro for my post)
I like your text. Even though you don't believe in evolution you can see beyond that and come up with an argument that doesn't need evolution to be wrong for God to exist.
I was a catholic until i was 13 years old, then i stopped being a catholic, or in any way religious, but i still believed in god (with arguments similar to those you use in your post), then i became agnostic and then atheist. Strikly speaking, i accept the fact that whe can't prove 100% there isn't a God, and that whe can't understand him, if there is one, good chances we don't. On those grounds i'm still an agnostic, but you can't prove any theory 100%, there's always a chance they're wrong. So i'm actually a skeptic. But i also accept that different theories have different proof, and so, different "probability" of being wrong. So, same way as i believe relativity and evolution are right, i believe that there is no God. Therefor Atheist. Anyway, what i wanted to say is, only when i was 17/18 i knew that some religious people didn't agree with evolution. I'm from a country where there's really not much people who are creationists. I never needed to argue in favor of evolution for a long time, and most people in my country don't interpret the bible literaly (until i met the ones who do). So you're post actually reminds me of my first religious discussions where evolution wasn't the center of discussion, and i believe that there should be more of those discussions (more philosophical).
(End of boring intro)
Evolution explains how we, humans, and all species became what we are. Doesn't really explain why there's life, with earth exists, or why the universe exists. And you're right, for a long time physicists have admited that spacetime was created in the big bang and that whatever created it was outside of spacetime and even very probably incomprehensible for human logic (because if you accept we're not perfect and that there are things we cant comprehend, and i know you do, you can also accept that there may be some kind of "order" that we can't understand). And because of that many people call whatever existed before the big bang and/or created the big bang, God. Well, if you do that then i believe in your god, because i believe in the big bang, and i believe there at least a possibility that it was created by something (i say this because you never know, there may be a theory that contradicts that possibility, advanced physics can be very counterintuitive some times, that's why i love it). But with this argument alone, you can't say that with that your God is the christian God. It could be, it could be a greek god, it could be allah, it could be the multiverse, a white whole, etc. There are many Gods and, more importantly, many scientific theories that fit in that description. So science does have a First Cause (it might not have a first cause to that first cause but we're not discussing that, you also don't have a first cause for God so by now me telling that the multiverse is eternal or god is eternal has the same validity).
But then you say that the order in the universe suggests a creator. Well, if there are other universes for instance, and depending on what kind of parallel universes they are, they could even have very diferent laws of physics. So the fact that this one has order, if that theory is true, is just a statistical necessity. If there are infinit, or a very great number of universes without any order we have to accept that it is then very probable (or even necessary) that there are many others with order. You don't need an intelligent designer here. Random creation of many many universes with random laws of physics would explain this universe's order. By now (i mean, in my post) we have only two theories and (still talking ONLY in my post) no proof for any of them. Then there's a 50% chance you're wrong. You're theory is possible but not necessarily right. So, you're argument is not by itself right. There are many other hypothetical theories like this one, some of them have proof, some of them don't, but all of them possible.
Now lets say there's order in the universe because we see order. We only know this universe, there could be one with more order (even if i can't be other universes, there's the possibility that this universe could've been created different) , more beautiful, etc. But because we only know this one, and we only can think inside this one, to us this is perfect order. We only see order because we evolve to see order, and no one can say that that's not usefull for a specie. As far as we can tell there's at least a little bit of order (laws of physics) but beyond that, we cannot compare this universe to anything so we can't judge its caracteristics.
Conclusion (if you don't feel like readind all of this, you can just read the conclusion)
So, we can't really say how fine tuned it is (only that it isn't completly random, unless reality is an ilusion), and the "God created the universe" theory is only one of milions of theories (some of them we can think about, some of them we can't, some of them we probably can't even imagine it), many of those theories with good/better proof then that one. And even if it is true the God theory, what God? What religion is right? Is any religion even right? It might be some kind of personal God we never thought of, or even something that's not even like anything similar to a God that created the Big Bang. It's possible but very unlikely. Or at least not necessarily true, your argument.