This is just a portion of what Dr. Greg Bahnsen wrote to clarify what he believes it means to say “Men know that God exists.” The following excerpt comes from pages 182–184 of Van Til’s Apologetic: Readings and Analysis:

The Character of the Unavoidable evidence for God. When we say that men “know” that the living and true God exists, we are (in part) asserting that they “have evidence” that justifies the belief He exists. A word should be added here about the general nature of the warrant for believing, to which we implicitly allude in claiming that all men know God.
We do so because of a common but simplistic (and thus misleading) tendency to make inferential or discursive knowledge the model for all cases of knowing. If Sam knows that milk gives him indigestion, he came to his conclusion through certain “steps of reasoning.” He recalled a number of past experiences in which indigestion followed his drinking of milk, but could not remember any cases of indigestion where milk had not been in his diet, so he made a general association and interpreted it in a causal fashion, etc. Sam did not simply look at milk and immediately apprehend its indigestion-producing quality (although some children claim to have this kind of intuitive ability when they encounter new vegetables); rather, he inferred the truth of his experience. Likewise, if Sam knows that 487 multiplied by 139 equals 67,693, it would be highly unusual if he did not gain this knowledge by making a mathematical computation. In a large number of cases, our knowledge of a proposition is warranted by a discursive process of inference. For example, all the union truckers are on strike; Sam is a union trucker; therefore, Sam must be on strike. Such inferential or discursive knowledge is common, but that does not mean that knowledge arises only from such reasoning. There are obvious cases of noninferential knowledge; it is implausible and artificial to insist that they must somehow be the product of an “unconscious” inference.
Surely there are times when one believes certain propositions with good reason, without inferring them from other propositions-as when one believes that one is typing with both hands, or believes that the music is painfully loud, or believes that one is not the same person as one’s neighbor, or believes the times tables in math. When Sam knows a black cat is in his path, he does not infer it from propositions about his sensations, about forms of appearance, about animal categories, etc. His knowledge is not discursive, following certain steps of reasoning to a likely conclusion; he immediately (without mediating lines of inference) apprehends the truth that a black cat is in his path. (We need not concern ourselves here with debates over how to account for such noninferential cognition, whether by linguistic conventionalism, behaviorism, an intuitive faculty, etc.) Such a nonpropositional experience (an acquaintance with an object) is not something mystical and ineffable; rather, people have the ability to express and define the experience propositionally (thus describing it and relating it to other beliefs so that it is available for reference, memory, assertion, inference application, etc.). The “immediate” apprehension may very well be caused (“mediated”) by natural factors, but the recognition takes place in the absence of discursive inference ( drawing a conclusion through the mediation of reasoning from premises).
When we encounter a person at the store and “know” that he is our friend Sam, our belief can indeed be warranted without being derived or reached by a series of mental arguments. computations, or inferences. The same is true when we directly identify his signature on a letter. There is evidence that justifies what we believe, but it is noninferential and direct. This claim should not be too controversial, but it does require some attenuation. in those cases where “knowing” is immediate and noninferential, we are speaking of the evidence as it is apprehended by a particular individual at the initial time of assenting to the proposition warranted by it. No doubt somebody else who is unfamiliar with Sam might not immediately apprehend that this letter is from Sam. And if someone should raise some doubt whether the letter is, after all, from Sam, the kind of “evidence” that would be brought forth to defend or vindicate the challenged belief would be discursive or inferential kind, rather than the initial evidence of direct apprehension.
Philosophers have argued for years over what kinds of things (or truths about what kinds of things) can be “known” or justified by direct apprehension, rather than by self-conscious process of demonstrations and inferences. Candidates have ranged from sensations and perceptions to universals, clear concepts, self-evident truths, and obligations. Van Til maintained, following the teaching of Paul in Romans 1-2, that all men have a knowledge of God that is justified by direct apprehension of His handiwork in the world and within themselves. Even without a discursive argument or chain of inferences from elementary observations about experience, all men see and recognize the signature of their Creator in the world that he created and controls, as well as in themselves as His created image. Van Til wrote, “Man is internally certain of God’s existence only because his sense of deity is correlative to the revelation of God about him. And all the revelation of God is clear.” This knowledge of God is mediated in the sense of being caused by the stimulus of the external world and man’s internal constitution, but it is apprehended immediately without argumentation, computation, or self-conscious reasoning.