The Universe is NOT steady state. It had a beginning, and it will have an end. What caused the Universe? There are several theories, but a common one is that our Universe is just resting on top of a membrane in hyperspace. The cause of the Universe may have been two membranes colliding. But what caused the membranes to exist? We don't know. Because even though our own universe had a finite beginning, hyperspace could have always existed, and it doesn't have to obey our laws of physics or causality, because physics breaks down when you leave the scope of our universe. Point is, there is nothing disproving the existence of God, and there is nothing proving his existence either.

Two words: membrane theory.

According to more recent "multiple universe" theories, the Universe could have been created by several theorized causes, including the collision of two universe "membranes". I don't want to go into too much detail on a comment, but if you research it online, you'll find information on it. Point is, this logic does prove that the Universe was caused by something, but you can't say that it's definitely God, beyond a doubt.