One of the more celebrated arguments for atheism is based on the concept known as Russell's Teapot. According to this analogy (also known as the Celestial Teapot), originally proposed by Bertrand Russell and recently reconsidered by Richard Dawkins, we can imagine that somewhere in our solar system is a small china teapot orbiting the sun. While there may indeed exist such a teapot, and we may have simply failed to detect it (so far), all the evidence at our disposal gives us no reason whatsoever to accept the orbiting teapot hypothesis. By analogy the existence of God is said to be a similarly failed hypothesis, not because anyone can definitively prove that God does not exist, but because we have no evidence to support the contention that God does exist. The idea is that in certain cases absence of evidence may as well be evidence of absence.
But behind that idea is another idea, a confusion about just what "evidence" is. Per the teapot argument, evidence is no more and no less than empirical detection of physical objects. Therefore the fact that no one has empirically detected the celestial teapot means there is no evidence for it. Whereas an eyewitness report, or a photograph, or an old grainy film clip, of an alleged Bigfoot at least potentially constitutes evidence for Bigfoot, a failure to provide any documentation of the Celestial Teapot means there is precisely zero evidence for the Celestial Teapot. This reductionism of evidence to "the thing itself" is what inspires skeptics to say things like "I'll believe just as soon as you show me your god," or "So where is your little god-thingy?", and the like.
Whereas admittedly such a restricted understanding of evidence would mean that there is no evidence for God, it would also mean that there is no evidence for scientific theories – nor even many of the phenomena those theories purport to explain. After all, no one can detect a theory with scientific instruments. "No one has seen God at any time," it's true. But neither has anyone seen a "general relativity" or a "quantum mechanics." These theories, largely mental constructs superimposed upon the observable world, are derived from, but certainly not reducible to, empirical observations of physical phenomena. In cases of scientific inference evidence is not a sighting or other empirical verification of an object, but data which makes a theory more probable than it would be otherwise (or more probable than alternative theories). By this account science is not naïve empiricism – mere collections of data – but more importantly, interpretations of the data and inferences drawn from them. In a sense the theories transcend the data.
I would also argue that in similar ways belief in God also transcends the data. This is not to say that Christian theism is a scientific theory. After all, God is not just another natural or physical or contingent entity, but rather the being upon which all other things are themselves contingent. Yet in principle, at least, God explains quite a bit. As Garvey states it:
If there is any evidence for God, it is by means of what God is supposed to have done – which means that that evidence can only be accounted for by God if we impute causal powers to God far above and beyond the ‘power’ to just sit there. And there is nothing that allows us to say what God looks like – if indeed God looks like anything at all. So, when we say that there is no evidence for the teapot, and when we say that there is no evidence for God, we are saying two very different things. In the first case, we are saying that there haven’t been any sightings; in the second we are saying that there is nothing for which God is the best explanation.
Of course it is this second sense in which Christians appeal to evidence. In religious experience, the arguments of natural theology, historical evidence for the miracle ministry and resurrection of Jesus, etc., there is sufficient reason to impute causal powers to God far beyond "the power to just sit there." Thus there are many things for which God is the best explanation. Thus there is abundant evidence for Christian theism.
 Brian Garvey, "Absence of Evidence, Evidence of Absence, and the Atheist’s Teapot," Ars Disputandi, Vol. 10, No. 1, p. 9-22.