Always looking to simplify my favorite arguments, I think we can make the Thomistic Cosmological Argument (TCA) even more accessible to readers than it already is:
1. Limited things exist.
I trust that this premise will be the least controversial. It will be important, however, to point out that I am using "limited" in the sense of "limited with respect to power." You and I have our limits, as do mountains, trees, solar systems, etc.
2. Every limited thing has a cause.
Why does some limited thing - say, a mountain - exist rather than not? We know that entities, like mountains, have various geological processes that cause their existence. Via induction, we may apply this principle to whatever is limited.
3. If there is no First Cause, then nothing will be caused.
Is the regress of causes found in nature limited or unlimited? Given that each of nature's other attributes is limited (e.g., the mountains), it makes the most sense to say that the regress of causes found in nature is likewise limited. This would require that nature has a First Cause, and confirms our usual illustration of a house requiring a foundation. Making nature infinitely old doesn't avoid this conclusion, either, since an eternal house would still need a foundation.
4. Therefore, a First Cause exists.
(4) follows logically from (1)-(3).
5. Every existing thing is either limited or unlimited.
(5) is true via the law of excluded middle.
6. The First Cause cannot be limited.
In support of (6), we know that if the First Cause were limited, then it would have a cause (see premise ). However, if the First Cause has a cause, then it wouldn't be first, which is a contradiction. It also doesn't do any good to ask the rhetorical question, "if everything has a cause, then what caused the First Cause?" For, premise (2) doesn't state that everything has a cause, but that every limited thing has a cause.
7. Hence, the First Cause must be unlimited.
(7) follows from (5) and (6).
8. Whatever is unlimited is supreme.
"Supreme" in this context means "unlimited and unique." The uniqueness of the First Cause can be demonstrated as follows. If there were two unlimited things, then there would be distinctions between them. However, things can only be distinct if one lacks something the other possesses. But, a thing can only lack something if it is limited, and the First Cause is unlimited. Therefore, the First Cause is unique.
9. Therefore, a Supreme Being exists.
If "being" is deemed too personal of a term, then the reader is free to substitute "entity" or "thing."
I'm honestly not impressed by objections to this argument. I think the skeptic's best bet is to reason that the Supreme Being is not a personal God, but something like "Nature itself" or some kind of similar Spinozean concept. Even if this alternative route is taken, the TCA still demonstrates the existence of an unlimited and unique First Cause, which I think is a victory for theologians and natural theology.