There are two problems with it. One is, that even this endeavor would be successful, it would never point to the God of Christianity. It would only point to some faceless “first cause”, “primary mover”, whatever, which does not necessarily exist today…
Aquinas also tries to show that the first cause is necessarily good, omnipotent, omniscent, omni-benevolent – all the good stuff

Not many of us outside the circle of Christianity may be convinced by these arguments – I among them – but, from there, one could go on to say “gee, all of these qualities sound awfully familiar to the God posited by Christianity” (which can work both ways, as there is a reasonable suspicion – especially for those who find problems with the arguments themselves – to posit that Aquinas may have been predisposed or biased to…find what he was looking to find, in the first place).
What even Aquinas never claimed to do is try to prove the Trinity or the divity of Jesus, nor hell or the existence of the devil – not without Scripture, at least.
The more serious problem is that Aristotle and Aquinas were totally ignorant of the “physics” of reality. Being ignorant, they speculated and came up with some “metaphysics”. They had no idea that “motion” is a relative term, that there is no difference between stationary existence and linear motion. …
My own reservations do not have to do with science, per se, but witht the logic of the argument itself. I see a few possibilities, here. One is that there is an uncaused cause. Another is that perhaps we should question our understanding of causality; is it possible that we are not understanding causality in the correct way? Certainly, it is possible. In making an argument, one is
assuming one’s understanding of causality is correct – whether the causuality of Aristotle
or causality as posited by modern science. Both could be wrong. Another question would be, in terms of any temporal aspect to the uncaused cause argument, “is it perhaps our understanding of time that is limited and incomplete?” This question has been posed by scientists and philosophers as regards the question “what existed
before the Big Bang?” The very question may not be sensical and may point to our own conceptual limitations.
In very general terms, it’s unclear to me whether the uncaused cause argument is logically sound – therefore, true – or whether it is more of a Zeno’s paradox kind of formulation, more along the lines of, “yes, it would certainly
seem as if there would have to be a first cause.” Of course, a not unnatural question to ask, in that case, is, what caused the
first cause? And if something that exists can exist
without an antecendent cause (namely, the uncaused cause) then why not the universe itself? Thus the possibilities, as I understand them, are:
- There may be an uncaused cause to the universe
- The universe may not have a cause, in any sense in which we understand causality
Notice I used the conditional “may”, which is perfectly respectable in terms of concluding that there is “insufficient information to know for sure” (a scientist like Hawking does not claim to have all the answers – for example, to the question, “what existed before the Big Bang” and is not certain that such a question even makes sense, within the context of our current understanding of time, or otherwise). I can’t posit an immaterial first cause that exists outside the unvierse because I do not
know that there is anything that exists outside the universe, that could fill the shoes of an uncaused cause. It’s possible there is, with or without the first cause paradox. But I can’t know this; I can’t know if my positing the uncaused cause would be like scientists positing the “ether” in 19th century physics (from wikipedia: Aether theories in physics propose the existence of a medium, the aether (also spelled ether, from the Greek word (αἰθήρ), meaning “upper air” or “pure, fresh air”[1]), a space-filling substance or field,
thought to be necessary as a transmission medium for the propagation of electromagnetic or gravitational forces. The assorted aether theories embody the various conceptions of this “medium” and “substance”. This early modern aether has little in common with the aether of classical elements from which the name was borrowed. Since the development of special relativity, theories using a substantial aether are not used any more in modern physics, and are replaced by more abstract models.]