The conundrum of a Creator God

One of the most common explanations of what God is, is that God is the Creator, and responsible for creating everything. That means everything that exists was created by God.

So, we have two propositions:

• God exists.
• God created everything that exists.

It follows that God created God. Does that sound right?

One of the most common refrains of people who subscribe to intelligent design is that the very complexity and regularity of life suggests that it needed an intelligent hand to be created. After all, entropy would suggest that you cannot get order from disorder, or so they claim. Here's the problem though. According to them, anything of complexity can only arise from something even more complex. God, therefore, must be significantly more complex than us. But, then the question is where did God come from?

If we argue that God always existed, why couldn't everything else have always existed? Why do we need a Creator?

Ultimately, if there is a Creator God, i.e. a separate entity that created us, the biggest conundrum is where that entity come from?