God Almost Certainly Exists I think that if we're inclined to pontificate (it seems an appropriate word) on the subject of the existence of God, and intend to come to any conclusion which might be described as based on a proof, we must content ourselves with "proving" nothing at all, or at most very little.
As is so often the case, definition is essential to any argument. If you want to prove that something exists, it's useful to define that something in the simplest, most abstract manner possible. The less to prove, the better. A creator God must, at the least, have caused the universe to exist. So, it's necessary, at the least, that there must have been something that caused the universe to exist.
Proof of that, according to some, is achieved by one of "Fat Tommy" Aquinas' "proofs" which is mentioned in the OP. That proof he borrowed like so much else from Aristotle.
However, if that "proof" is, in fact, a proof, all it establishes is a "cause" of the universe. But it seems that we can't know anything significant or even meaningful about that cause. It might be argued that such a cause must have existed before the universe did. That could be problematic, though, as "existence" as we know it as concept we define based on characteristics and events which take place in the universe. So, for that matter, is "cause." In fact, anything we know, anything we think, feel, speak of, observe, describe, or do, is based on what takes place in the universe.
So, we can't prove or infer that this "cause" has any of the characteristics we normally attribute to God.
We can't say that it is within us and everything else. We can't say that it's wise, loving, all-knowing, all-powerful, that it is Jesus (or whatever), that it listens to and answers prayers, that it requires we perform certain rituals, that it regulates our sexual conduct or other conduct, etc.
To prove such things about the "first cause" requires much more in the way of proof. I can't understand why the "proofs" of God's existence are of significance to anyone as a result. Believers in God as we normally think of God are reduced to the sad tactic which has been employed by Christian apologists for so long, which is merely to claim that the presumed first cause is Jesus and has all the traits we want it to have, consistent (sometimes) with what we think of Jesus.