Berlinski grasps intuitively that God exists from the spirituality of humans, the Big Bang, and the complexity of life. He doesn't understand that the logical proof of God's existence is based on the finitude of finite beings. We are finite beings because we have free will. Free will means we possess a center of action. This means we are unified with respect to ourselves and separated from other beings. In short, finite beings exists. A finite being needs a cause. If every being needed a cause, the universe would not be intelligible. Hence, an infinite being exists.
I consider the above deductive process a proof, not an argument, because there is no need to make a decision about God's existence. The only decision that has to be made is whether God has communicated himself to mankind.
The other weakness of Berlinski's book is that he swallows the idea that there is some kind of scientific controversy about evolution. As my review of Kennth Miller's book proves, all scientists agree that Darwinian evolution only explains the adaptation of species to the environment.