Atheism is one of the key pillars of objectivism, but Rand and her associates do not offer any “original” arguments to prove that god does not or cannot exist. Stephen E. Parrish engages with the objectivist claims on atheism in his article “God and Objectivism: A Critique Objectivist Philosophy of Religion,” (published in The Journal of Ayn Rand Studies, Volume 8, Not. 2 — Spring 2007). He notes that while the objectivists have good arguments on the subject, they never try to grapple with the arguments of the theists. They have made no attempt to answer the arguments of Thomas Aquinas.
Parrish begins his article with these lines:
"Ayn Rand is well known for her atheism. Writing primarily from the 1930s through the 1970s, she expressed disdain for the whole concept of God, and of religion and supernatural in general. This was in a manner consistent with the mainstream philosophy of the time. To be sure much of the mainstream rejection of God was based on concepts like Logical Positivism, Linguistic Analysis, or Verificationism. Though Rand rejected these philosophies, and for good reasons, she agreed with them on the question of the lack of viability of theism."Parrish notes that in the last few decades there has been a revival of interest in philosophy of religion. The field of philosophical theism has been resurrected through the works of several philosophers. (I recently read Prof. Edward Feser’s Five Proofs of the Existence of God). Since many of these works have appeared after Rand, she cannot be expected to respond these developments, but what is surprising is the lack of reaction from her objectivist followers. Objectivism, it seems, is failing to keep up with the work that the contemporary philosophers of religion are doing.
He ends his 42-page article with these lines: “every Objectivist objection to theism or supernaturalism is fallacious. What has basically been done is that Objectivists have assumed certain philosophical positions to be true, compared them to theism, seen that they conflict, and then dismissed them as false. Rarely are responses that theists could make considered.” I think, Parrish has written a fine critique of the objectivist view of god and religion. You may disagree with him but his arguments are worth examining.