Here is a great citation from the late Dr. Greg Bahnsen on unbelievers knowing and not knowing God.
We will take Sam as our hypothetical unbeliever. When we say that Sam does not believe in (or know) God, we are describing him according to certain features of his behavior and thinking: for example, his moral conduct and attitudes, his refusal to glorify God, and especially his profession not to believe in God. After all, Sam acts and talks like a person who sincerely disbelieves; indeed, he argues vehemently against believing in God’s existence. However, the fact of the matter is that Sam actually does believe in God. When we say that he believes in God, we are (in accordance with the diagnosis of God’s word) describing him according to certain features of his behavior and thinking that manifest belief: for example, his living in terms of some kind of moral standards, his acceptance of the need for logical consistency, his expectation of uniformity in nature, his fear of death, and his assuming of freedom of thought. As in the case of believers, we say that Sam knows God in the sense that he has justified, true beliefs about Him. So then, it turns out that Sam’s belief in his own unbelief is mistaken. He rationalizes evidence, motivated by his desire to avoid facing up to God, whose condemnation he fears and whose authority over him he resents. Nevertheless, he sincerely and constantly pursues unbelief as his self-deluded life’s project.
It thus appears that the unbeliever works with two different sets of fundamental beliefs or presuppositions, one acknowledged and another unacknowledged (or denied) – one that makes his regulating ideal, and the other which makes it possible to know anything. He inescapably knows the truth (one set of beliefs) and yet suppresses it (endorsing a second set of beliefs). Van Til’s Apologetic, 451