Dawkins never claims to be able to prove that God does not exist.
Ochams razor always has to be offset with the principle of comprehensivity. A theory must be the simplest one that will cover all the salient facts. In the case of God there is never going to be an agreement on which facts are salient. Is my experience of God a salient fact? - it may be to me but it cannot be to you.
Although people like to talk about objective evidence, evidence is that which makes evident and there must be someone to whom it makes something evident. As Polanyi says knowledge is not subjective or objective but personal. That is what makes these debates so interesting and ultimately so frustrating.
We can get a large measure of agreement on where a set of scientific evidences is pointing but there is no logical path which can lead from evidence to truth as long as the thing to which the evidence is pointing cannot be directly encountered. So the judgment that a theory is true is always a personal judgment.
Hope this is helpful.
