It may be worthwhile referring to the First Vatican Council in the statement on the provability of the existence of God which is very likely infallible from the point of view of the Catholic Faith. See
here for the statement.
I have developed a proof of the existence of God but I am not sure whether there are any flaws in it. Perhaps you could have a look at it.
I started developing it when I could not understand how to assume the premise used in Aquinas' First-Cause proof stipulating that all things had a cause (I think some ppl here had the same problem).
It is shown below in a mathematical manner as well as in a prose form.
View attachment 6998
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Part 1 - Proof of the Existence of G-d
For every two things, there is a relationship of sorts, between the two things. For example, one can say that there is a relationship between two objects a million miles apart via space. The relationship is such that either both things depend on something 'outside' of themselves (in the prior example, the dependency would involve space, a separate thing) or one of the things is caused by the other. This relationship must exist, by virtue of their co-existence in the same universe. Something ties all things together - nothing is completely isolated. Take for example the colour red, and the song of a bird. It might seem as though there is no relationship between them. However, something makes the colour red not the song of a bird and the song of a bird not the colour red. This relationship involves distinguishing them into quite different existences. It is like a grand person sorting the two things into two different boxes representing different categories; the person then acts as part of a link (relationship) between the two things.
There cannot be two uncaused causes, since, as stated, for every two things, there is a relationship between the two things. An uncaused cause implies no dependency & a relationship would imply at least one dependency. Furthermore, there must be at least one uncaused cause because otherwise, we would have a universe of just dependencies on other things and this cannot exist. It cannot exist because the dependences would never be fulfilled; for every dependency, another dependency would need to be fulfilled. Therefore, there must be only one uncaused cause and we call this uncaused cause, G-d.