Attn: Theists - What would it take to prove you wrong?

[Sword of Christ]

But you claim your god is eternal. Equally logically, I say the universe is eternal.

...But we know the universe isn't eternal though. Big Bang? The beginning of time and space? The cosmic background radiation? The laws of thermodynamics?

You eternal god has no cause, so if not caused it can't exist.

God isn't meant to have a cause God is the cause, being the cause of all things that are caused is the idea. Without a cause nothing can be caused.