Dawkins is using scientific method (along with faulty logic) to prove God doesn’t exist.
If science cannot prove A, then:
Scientific evidence cannot prove A, then:
Lack of scientific evidence to prove A proves nothing
I’m no Dawkins lover my any stretch, but let me just play “devil’s advocate” here.
I don’t think Dawkins is claiming that science “disproves” the existence of God. I think he is merely saying that science renders the “hypothesis” of God unnecessary, and he *chooses* not to believe it. That my impression of his position, anyway.