The argument for existence of God that's based on the design of the universe is called the Teleological Argument. It says:
1) Anything designed must have a designer.
2) The universe has a purposeful, complex design.
3) Therefore, the universe must have a designer.
Statement #1 seems intuitive enough. If we found a computer in the desert, we would know it was not randomly formed by natural processes from silicon in the sand. Rather, we would know that it had been purposely designed by an intelligent designer. But what about Statement #2? Was the universe designed?