Contingent things exist.
Each contingent thing has a time at which it fails to exist.
So, if everything were contingent, there would be a time at which nothing exists.
If the world were empty at one time, it would be empty forever after.
So, if everything were contingent, nothing would exist now.
But clearly, the world is not empty.
So, there exists a being who is not contingent.
So, God exists.