Proof by reductio ad absurdum

Assume there is no first cause.

"But if we remove a cause the effect is removed." (Aquinas IP3 168a)

So, if there is no first cause, there is no second cause, and no third cause . . . and thus no causes at all!

But there are causes (i.e. something things are causing other things).

But this is a contradiction ("There are causes but there are no causes").

So, by reductio, the assumption is false.

I.e., There is a first cause.

If there is a first cause, then that first cause is God. [linking claim]

Therefore, God exists.