Before we can answer the question regarding whether we can know about the existence of God, it is important to understand the meaning of “know” or what it means "to know". For example, a “theist” or believer in God affirms we can know that God exists. An “atheist”, on the other hand, denies the existence of God but affirms that what we can know about God is that he does not exist. Both positions claim knowledge about God is possible, though the positions are on opposite ends of the philosophical spectrum.
“Agnosticism” is different from theism or atheism, in that the agnostic position claims that any knowledge about God either does not exist or if it does, it cannot be discerned. Therefore, any discussion about the existence of God is meaningless. We cannot know either way. It might be that God exists and it might be that he does not. Granted, depending on certain presuppositions, some agnostics might "lean" toward a belief in the existence of God or they might lean toward a denial of that existence. Whatever leanings an individual agnostic might have, the overall agnostic position affirms that all we can know about God is that we cannot know anything about God.
The controversy over whether or not we can know about the existence of God concerns whether we can know about something unseen from the evidence of what we can see. Fortunately, knowledge about the existence of something is not always based on whether we can see it. For example, though we have never have been to China, we can still know that China exists. If that is not the case, then we would all have to travel to China before we could confidently conclude that China does indeed exist. Another example is, none of us have actually seen our own brain but who would reasonably argue that because we cannot see it, we cannot be sure that it exists? Evidence of what we cannot see is based on the strength of the evidence of what we do see.
Even scientists who embrace the "Scientific Method", which states that the conclusions of science must be confined to what is personally experienced or tested, still cannot resist applying the conclusions of their experiments to what they have not seen. An example would be the "Big Bang" theory. This is why the claims of agnosticism regarding the existence of God have little substance. It is not contradictory to affirm that we cannot know anything about the existence of God, while at the same time affirming that we can know something, even though what we can know is that we cannot know anything about God's existence? In more simple terms, how is it possible to know that we cannot know anything?
Therefore, the ability to know about something that we cannot see or experience is logically possible. This truth in regards to the existence of God implies that though we cannot see him, it is possible to know from an examination of the evidence whether or not he exists. A discussion of that evidence is another matter altogether.