Here’s how I explain the Catholic explanation of the existence of God in ~500 words.
(Had to cut the intro to fit on the forum)
Prima Via: The Argument of the Unmoved Mover
Aquinas uses the term “motion” to describe any of the many kinds of change within the universe, but the argument works the same regardless of these specifics. It goes as follows:
P1) Change within the universe exist because of an external cause
P2) There cannot be an infinite regression of external causes.
P3) Therefore there must be an uncaused cause.
From the Catholic perspective, this “uncaused cause” is described as God. It’s important to recognize that this argument describes an “accidental” series of causes because the existence of member B of the series necessitates member A for its creation but not its continuing existence
Secunda Via: The Argument of First Cause
This argument is largely very similar to the previous but the difference lies in the important detail of an “essential” cause.
P1) Everything we see has an essential cause.
P2) There cannot be an infinite regression of essential causes.
P3) Therefore there must be an uncaused essential cause.
An “accidental” series can be described as temporal but an “essential” series is better described as hierarchical. For example, a person’s existence occurred because of their parents, and their parent’s parent’s and so forth; but a person’s existence occurs because of cells they are made up of, and the atoms that make those up, and the particles that make those up and so forth. In the first, the parents don’t need to exist anymore, whereas in the second all parts must exist at once for the person to exist.
Logically, this necessitates the continued existence of a first cause (AKA God) that more fully fits the description proposed by the Catholic Church. This is because this God must permeate everything and be theoretically able to intervene (being the basal cause). IE omniscient and omnipotent. It also necessitates this God (in a personified sense) willing the continued existence of the universe implicating some sort of love (in the theological sense) for it. Finally, with the philosophical assumption that purpose comes externally (typically by a creator) this means that God is the origin of purpose and morality making “him” inherently omnibenevolent.
This still requires a significant jump to Catholicism specifically, as this only lays the groundwork by arguing for God. However, the version of God necessitates allows for and heavily suggests the presence of “revelation”. As CCC 287 says “Beyond the natural knowledge that every man can have of the Creator,124 God progressively revealed to Israel the mystery of creation”