He proved it in the Five Proofs:
[li]The Unmoved Mover.[/li][li]First Cause[/li][li]Argument From Contingency[/li][li]Argument From Degree[/li][li]Teleological Argument[/li][/ol]
Now, one by one.
The Unmoved Mover goes like this: Some things are in motion. Things can’t move themselves. An infinite chain of movers is impossible. Therefore, there must be an unmoved mover who moves all things. This is what we understand to be God.
The First Cause: Kinda the same thing, but with causation. All things have a cause. Infinite chain of causes? (imitate “wrong” buzzer from “Family Feud”) Can’t happen. Therefore, there must be a chain of causes that is the cause of all causes. This cause is understood as God.
Contingency Argument: Things in the universe either exist or don’t. The things that exist are either contingent or they aren’t. It is impossible for everything in the universe to be contingent, otherwise we end up with a time where nothing existed, and nothing could bring forth existence. This is obviously false because we know we exist. Therefore, there must be a necessary being to bring forth existence. You guessed it: God, or who we understand to be God.
Degree Argument: Different kinds of perfection may be found in varying degrees across the universe. These degrees factor in a sort of ultimate standard of perfection. Perfection, therefore, must have a pinnacle. One guess what this pinnacle is.
And, finally, the Teleological Argument: All natural bodies follow laws of conduct. Some of these are unintelligent (but others not). Laws of conduct are characteristic of intelligence. Therefore, there exists an intelligent being that created these laws. One guess…
Now, this makes sense based on what we have learned since Aquinas’ day. We know for a fact that there was indeed a beginning for the universe. There are indeed bodies that follow laws of conduct. (Think about animals in the forests and the jungles, or, for something more inanimate, rock formations and their erosion.) Can a rock formation move itself? Of course not! Can we move ourselves? Of course not. We require muscle and bone and a functioning brain in order to do so. There are things that don’t exist or do exist. “Cognito ergo sum,” to borrow from Rene Descartes. Therefore, it stands to reason that there must be a First Cause, otherwise existence itself cannot exist.