Thank you very much. Yes, actually, it really does sound like a kind of anthropological proof, although from what I remember it is built differently.
Why do you think it is weak?
Is it because it may be explained by saying that God is a composite of earlier concepts? (What I was trying to say is that this is almost impossible, because people דווקא don’t usually define Him, and nevertheless they understand Him.)
Or because there is no identity between a concept and its realization?
Or something else?

First, mistaken cognition is possible. There is something in reality that I see differently from what it is, and as a result a concept is formed in my mind that does not really exist (is not realized) in reality.
Second, concepts can be synthesized from other concepts. I do not see any problem with synthesizing the concept of an omnipotent being who created the world and even gave the Torah. What is the difficulty with that? Ability is something we understand, and extending it to unlimited ability is not some impossible leap. Creation ex nihilo is unfamiliar to us, but again, that is an extension that I do not see as problematic.

The point is that here you are not seeing something else in reality…. (After all, you do not physically see God the way you see a table, so that you could say this is an object that was accidentally formed—how much more so when so many people grasp God, or something, even if you do not say it is exactly the same thing one-to-one [say, as with approaches of idolatry], still there is no doubt that this is something much more fundamental in humanity as a whole.) So it seems strange to say that there is something in reality that you see differently from what it is, when you do not see anything at all.

Second, it is true that concepts can be synthesized from other concepts, but first, as I recall, even according to your approach you would not claim as a default about every concept that it is synthesized unless proven otherwise.
And in any case, the main point is as I already emphasized before: people do not really grasp God as “an omnipotent being who created the world and gave the Torah”; rather, they have an *experience* that perhaps corresponds to those properties of the concept (and even that, only if you back a person into a corner will he say so). So most people generally do not elaborate in descriptions at all, or hardly at all, regarding the concept of God.
So in practice, that is exactly the claim: most people do not really define Him. And nevertheless they talk about Him in a way that is disproportionate compared to another object that we would expect, if it were so undefined, people would still talk about so much (if it did not exist). Therefore it sounds even stranger to say that this is a synthesis of other concepts.

(By the way, the concept of omnipotence is not exactly a familiar concept, and that already ties into the anthropological proof. דווקא creation ex nihilo is not exactly atheistic “something from nothing,” because God is an existent in Himself, so it is not essentially different from creating an electron in the brain by free choice, as you put it [though there there is an offset from the belly fat :)], and perhaps this is built on a lower “spiritual” layer that takes care of coordinating things, just as it takes care of offsetting the positive charge with the negative one that is created randomly.)