Can we "know" that God exists? - Definitions.

The mitzvah of Yedias Hashem requires that a person use his rational faculty and accept through it that God exists. That is what the word Yediah – knowledge means. To do that we have to first develop a basic concept of what God is. Here is Rambam in Moreh 1:35

For in the same way as all people must be informed, and even children must be trained in the belief that God is One, and that none besides Him is to be worshipped, so must all be taught by simple authority that God is incorporeal; that there is no similarity in any way whatsoever between Him and His creatures: that His existence is not like the existence of His creatures, His life not like that of any living being, His wisdom not like the wisdom of the wisest of men;

(Even children must be indoctrinated that God is different in all senses and that even the word “existence” as applied to Him is different!)
Rambam further on finishes:

Anything predicated of God is totally different from our attributes; no definition can comprehend both; therefore His existence and that of any other being totally differ from each other, and the term existence is applied to both homonymously, as I shall explain. This suffices for the guidance of children and of ordinary persons who must believe that there is a Being existing, perfect, incorporeal, not inherent in a body as a force in it-God, who is above all kinds of deficiency, above all affections.

Rambam tells us that even the simple need to be taught that God is different. When they grow up and the simple become wiser and want to “know” God, they will have an idea of what they are trying to understand. Unfortunately, because of reasons that I do not want to go into here, we have not lived up to Rambam’s expectations of how God should be represented in the general population’s imaginings. A pious Jew is considered more religious if he believes in a God that “exists” in a way that He can be pointed out, “felt”, intuited etc… When that Jew is confronted with the need to prove the God that is a figment of his imagination, he is unable to do so. He must resort to “faith” or some other stratagem. He has to allegorize “Yediah”. That is why Rambam insists that the correct image of God needs to be developed in the mind of children and the simple.