St. Augustine’s proof of God looks something like this (this is from memory, so forgive me if it’s totally wrong):
1) The nature of Truth is to be held in a mind
2) There is necessarily Truth
3) Ergo, there is necessarily a mind which knows this Truth
Now, there couldn’t be Truth without a mind knowing this Truth, so this Mind must know all (2,3); this Mind would be omniscient; further, the Mind’s self-necessity would require it to be omnipotent; further, no Truth could exist beyond itself, so it must be coextensive with all domains of Truth, so it must be omnipresent; and etc. In other words, this Mind is God.
I think I have a similar idea;
4) It would be true that the universe doesn’t exist if the universe didn’t exist
5) It is conceivable that the universe didn’t exist
6) However, if no universe exists, then the truth must exist in something that exists necessarily
7) Ergo, there exists a necessary Being
I think the controversial premise here is (6). My argument for the soundness of (6) would be as follows;
6.1) Nothingness cannot offer any truth value
6.2) But there must be truth value
6.3) Ergo, there must be something that offers truth value
Now, a necessary being is what all understand as being God. Further, the universe does exist, and as it is conceived to be contingent it must be contingent in relation to God (the necessary Being). So, the universe was brought into existence by nothing other than God, and so the ability to bring the universe into existence stems only from God, and so God must be omnipotent, as no power came from elsewhere, and all power originates in God.
I don’t know about how the other attributes would be proven, but perhaps its similarity to Augustine’s proof could offer something. I’ll have to think on it some more.
St. Anselm’s ontological proof is much better, in my opinion.