To know there is no God one would have to know and experience all things, because God could be within an area that they do not know or in which they have not experienced. Even if one were to have all the knowledge and experience of 50% of the Britannica, that would mean that there is 50% they cannot know nor have experienced. So to know God is not, one has to know all.
To know there is no God, one would have to be in all places simultaneously because God could or have revealed Himself in a place where you are not (even to someone now, somewhere else).
You would have to have known all and been everywhere during all of the past, the present, and in all possible futures in case God was revealing Himself when you were not.
Finally, you would have to be aware of all that which is and/or has been known or experienced by all individuals of all times, in case He had revealed Himself to only certain peoples, at certain times.
Now this is rational and logical but only the tip of the iceberg but it should suffice…
So in effect, to know there is no God, you would have to be omniscient, omnipresent, and eternal, and able to experience the experience of all others, for any who may be able to receive illumination or revelation that God is. So to believe with conviction that there is no God, one then has to be exactly what is called God thus proving God IS.
I found this one interesting because it reminds me of the Universal Law of Uncertainty that I only recently learned about. Basically, it states, that you can't know that you don't know. The example I like to use is the Americas. When they decided to set sail across the Atlantic, they thought that they would find India and China, because they didn't know the Americas were there. So how could they know that they didn't know of the Americas existence without knowing about the Americas?
Let's take it a step further. When people complain that God should prove he exists, it isn't totally possible. If we use the term God to mean an omnipotent, omniscient, and immortal being. A very powerful being could prove that exists and has powers, but couldn't prove that it was God by that definition.
For example, we only live about 100ish years, if we're lucky, so how could God prove that he will never die if we don't live that long to see it? How could God prove that he is omnipotent without displaying for us every single power that could ever be? Again, we don't live long enough for every power to be shown like that. And how could God prove that he is omniscient unless he shares with us everything that could ever be known? But if he did share with us everything that he knows, how could we know that it was everything?
Let's take the Law of Universal Uncertainty one step further to the bad territory. How does God know that he knows everything, if there is something even he is unaware of, then he wouldn't know that he doesn't know.
Perhaps there really is a multiverse of parallel universes out there, and each one has a being that created the Universe inside it. That being has ultimate control over everything inside that Universe, but is unaware of any other powerful beings in other universes. That being would believe that it is omniscient because it knows everything about his universe, but it turns out there is more.
What's more, how could that being know that he is omnipotent? Unless he performs every power that could ever be performed, he can't know that he is capable, and if he is unaware of other powers, such as traveling between the parallel universes previously mentioned, he wouldn't know that he doesn't have a power that he doesn't know exists.
And what's more, how can that being know that he will never die? That being may look as far into the future as he can, and never find a limit, but until the end of an infinite number of years passes, he can't be sure that something won't change because he doesn't know until that point in time that his predictive powers are infallible.
So in short, we can never be sure that God exists or doesn't exist. But at the same time, even God can't know if he is really God.
So if a being claims to be omnipotent, omniscient, or immortal, he must either be unaware of this principle of uncertainty which means he is not omniscient, or is being dishonest because he knows that can't be certain that he has these qualities. Of course there is a chance that this being is omniscient, omnipotent, and immortal, but he would just be lucky to be right if it were true, it wouldn't really be a matter of fact for him.