I think that assuming the question in the OP dismisses or attacks God is a weird reading. What it really does is showing our limited capability to provide proof, which is actually a fact.
Think about this: language is our means of communication and reasoning, most of our sciences assume not only around logic, but also explicit rules. When we talk about math, there are always some axioms that cannot be proved, the source of math if you will, the context that puts logic into perspective.
Any language or method has an inflexible source, a part that cannot be questioned without effectively dismissing everything. Those are our systems, they always work from a starting point. And God is assumed to be the source of it all. There is a chance that, because of our systems, God is effectively impossible to prove or that even finding a proof of God would disprove His part as the origin of everything.