Question: Objectivism rejects the existence of God because it cannot be proven by our senses—in other words, God-believers must bear the "burden of proof," which, of course, they cannot provide. However, adherence to Objectivist philosophy does not require omniscience. Although "[m]an's reason is fully competent to know the facts of reality," one can know that man will never know all of the facts of reality. (Consider that the universe is continuously expanding, and, according to some astrophysicists, expanding at a progressively faster rate.
Given that man does not know everything now about the universe, it is logical to conclude that man will never know everything.) Accepting that man is not omniscient now and never will be, how can it be considered "unreasonable" to accept—not blindly, mind you, but after careful consideration of all of the possibilities—that which cannot be disproven? If reason truly is the epistemology of Objectivism and rationality truly is man's greatest virtue, how can Objectivism readily dismiss any idea that can neither be proven nor disproven? Is that not one of the noblest purposes of our minds—to strive to discover that which is not known?
I hope you have read D. Moskovitz's answer on agnosticism. If not, you can find it here
You are right: we will never be omniscient. And indeed, no being can ever be omniscient. "Omniscience" is a concept like "infinity:" it represents a direction one might head toward, but it is not a goal that anyone or anything will ever reach or ever can be.
You seem to be saying that because we are not omniscient, we cannot disprove that there is a God as the religions speak of one. As the answer “Atheism, Agnosticism, and the Arbitrary” explains, this is simply demanding that the atheist prove a negative. You don't demand that to disprove the existence of gremlins in your house every night, and with good reason. No more should we demand it for God.
We do face the unknown. How will we learn more and discover what we did not know before? We will do it by objectively integrating the facts that we come to know, using rigorous logic (both inductive and deductive). We certainly will not do it by accepting random claims as if they were true, simply because they sound attractive or because other people believe in them. Objectivists are atheists because by the very means by which we can uncover what is now unknown we must accept that we have no reason to think God possible or even logically conceivable.