You said if God began to exist, then he wouldn't be God. You are saying you know God is a being who need not to be created, as if you personally know him and his past!!

How do you KNOW God has been there forever, or appeared suddenly, or whatever. Every single idea behind God's origins is pure fiction made up by people!!

For doing so you'd need:

A. Prove God exists, as physical or metaphysical entity.
B. Ask him if he has been here forever or other being created him, or how he came to exist
C. Get an answer from him