It has been argued, by those who believe God does not exist, that since a belief in the existence of God is merely a matter a faith, and that there is no proof, then this belief is irrational. However, it is just as much a matter of faith to believe that God does not exist, as it is to believe in God s existence. The simple truth is that we do not know, and that goes both ways. We do not know that God does exist, nor do we know that God does not exist. No matter what we believe, on this issue, it is still a belief, not knowledge, so as a belief it is a matter of faith, either faith in existence, or faith in non-existence. If faith is irrational, as contended by those who believe God does not exist, then that faith in God's non-existence is equally irrational.
Belief and Non-belief are actually the same thing
Belief and non-belief are nothing more than the flip sides of the same coin, therefore a non-belief is the same thing as a belief, simply in reverse. The atheist argument that they do not have the burden of proof for their belief is a cop out. It is nothing more than an excuse to justify their belief without having to prove it. When an atheist says they know there is no God, they overstate their position just as much as when a theist says they know there is a God. It is not "knowing" that either are doing, but believing. To know a thing is to have direct experience, verifiable knowledge that can be measured and/or demonstrated as real. If a concept or idea is not directly known, then it is a belief. Therein lies a huge part of the problem with a great many folks on both sides of this debate. We tend to mistake belief for knowledge. When we sift through all the stuff in our minds and separate our beliefs from our knowledge, we find that in point of fact we know very little. The vast majority of it is a stair step pyramid of beliefs built upon each other. This includes non-beliefs. They too are a part of the pyramid of beliefs, as are theories and hypothesis. Another part of this debate which has an extremely problematic nature is the way some people treat theories. When one treats a theory as if it were a fact that is an error. Theories are not facts, they are a form of belief. They are beliefs, which have a body of evidence to support them. However, as long as any body of evidence could be interpreted with more than one theory, then those theories are not conclusive, thus inconclusive possibilities, and should not be treated as if they were factual knowledge. Theories come and go, based on the acquisition of knowledge. They are often revised or even discarded when new evidence comes to light and factored into the previous evidence upon which they were built. Like any belief, a theory could be wrong, but knowledge is constant and unchangeable. The greatest error that any theoretician can make is to cherish their pet theory so much that when contradictory evidence comes to their attention, they throw that evidence out, cover it up, or label it "anomalous", and then deny the existence of that evidence. That is the reaction of a dishonest theoretician.
Same logic works both ways
The logic I use is exactly the same logic as the atheist. A belief without proof is irrational. Both beliefs, that God exist, and that God does not exist are without proof, therefore both beliefs are irrational. The only rational position to take is that God may or may not exist, and we in our limited perceptions of reality are incapable of ever knowing with certainty one way or the other. We should, however, consider ourselves free to speculate on the topic profusely, if we are so inclined, and I am so inclined.
Can we fully comprehend the infinite?
In our place here on Earth, with our finite existence, we can never fully comprehend the infinite. We can imagine it, but that is not the same as comprehending it. So, if God does exist, and has an infinite nature, as some beliefs contend, then we will never be able to truly comprehend such an infinite entity.

Can we really comprehend true nothingness?
Conversely, if God does not exist, then God is null, or nothing. We can somewhat mathematically represent nothing as 0, and while the concept of 0 is very simple to us, it does not completely characterize total nothingness. In philosophical circles nothingness has been explored. Even there the scale of that nothingness is limited to "local" levels, delegating the idea of infinite nothingness to the realm of impossible, since observable reality indicates that there is something. Since there is something, including the observer, then we do not have complete nothingness. But the philosopher's question remains, why is there something rather than nothing? Just as we can not fully comprehend infinity, likewise we can not fully comprehend true nothingness. As a result of this awareness, either way it is a matter of faith, whichever way you believe. Consequently, both beliefs are equally irrational, simultaneously. This is especially true by the atheistic argument, that to believe something without proof is irrational. For just as those who believe in God's infinite existence, do so without proof; likewise those who believe in the nothingness of God's non-existence do so without proof. There simply is no proof either way, so no matter which of these options you believe, you believe it without proof. One would think that the opposite of an irrational belief would be rational, yet both beliefs exist without proof, so both beliefs are equally irrational. Such is the paradox of this debate, that each of these opposite beliefs can be equally irrational, at the same time. Make no mistake, there are many pieces of evidence that people on both sides of this debate can give for their arguments, but evidence is not the same as proof. In spite of all this evidence yea or nay, when it comes down to actual proof, there simply is none for either side.