Science studies the physical universe. If God exists, and is the creator of the universe, by definition He is not a physical object within the universe, and cannot be studied by the scientific method. Science can say nothing about the existence or non-existence of God.
Even Dawkins says God “probably” does not exist, he does not claim to have disproved the existence of God.
Dawkins is a biologist and his argument is mostly between evolution and creationism. This argument was over for most thinking people in the 19th century. I suggest we turn to 20th century cosmology for a more enlightened view.
This shows that, starting with the big bang, and evolving according to the laws of physics, the universe eventually produced human minds who can understand the laws of physics, and also almost universally have some religious sense. In the case of the two latest widespread religions, Christianity and Islam, this religious sense includes a belief in a creator god.
So, the existence of human beings who can understand the laws of physics and believe in God is a property of the laws of physics.
Furthermore, it can be shown that, if the laws of physics were slightly different from what they are, none of this would happen.
How did the laws of physics acquire this remarkable property? As a scientist I adopt as a working hypothesis the simplest explanation that fits the facts: that God put it there.
There cannot be a proof of the existence of God, but I conclude with confidence that God very probably does exist.