Explanation of Alter Rebbe's proof of G-d?

Question

I heard recently from a Rabbi's speech (a.k.a., I don't know the actual source) that when the Alter Rebbe was in prison in Russia one of the Russians there asked him to prove the existence of G-d.

So the Alter first asked him to think of something that doesn't exist, the Russian said: a flying cow. The Alter Rebbe then said that that's incorrect, because a cow exists, and wings exist, he's just putting two things that already exist together, but it's impossible to actually think of / know about anything that doesn't exist, so the Alter Rebbe concluded that since we know about G-d, he must exist, because we know about him, and it's impossible to know about something that doesn't exist!

When I first heard this it sounded pretty good, but then I thought: why can't you just respond that he know of human creators of art (for example) and the "know" about G-d is just to consider everything as like a big art piece, and then to imagine some bigger creator, so it would just be like imagining something that does already exist, a human creator, and putting it in another perspective.

So I'm not trying to challenge the existence of G-d, chas v'shalom, nor am I challenging the wisdom of the Alter Rebbe, but I was trying to understand this particular proof from the Alter Rebbe (and the Rabbi I heard it from said it was found later in the Rishonim). So if anyone either #a can explain why it can't be refuted from the above or #b just find the source of this story somewhere ('cause it might clarify things to see it inside), then that would be the #1 answer.

EDIT just to clarify, the context in which this story was said was to explain the following: There's some parts of G-d we can actually know about, like how He creates the world(s) etc., like it's actually possible to know about / imagine the energy that gives life to every being, that's something we can comprehend, know about, imagine, etc. so relative to that level of G-d, it's considered an "existence", hence the Alter Rebbe's proof that G-d "exists", since it's referring to that aspect of G-d, which another aspect of G-d (which isn't at all related to the Alter Rebbe's proof) is that aspect of G-d that's totally removed from the world(s), it doesn't create them at all, it has nothing to do with actively giving life to the world, and regarding that level of G-d, it's actually not at the level of "existence", because we can't know about it, and (the Rabbi I heard the speech from goes on to say) these two levels correspond to "Memale" and "Sovev" as discussed in Kabbalah etc.

but anyway, the Alter Rebbe was just trying to answer the question of a Russian "How do we know there's a G-d at all!" and to that question the Alter Rebbe just gave the proof simply about since we know about it, it must exist (and he was only / simply referring to the first level "Memale", since he didn't want to get into deep Kabbalah with this Russian, just to simply explain that there is a G-d at all).

My question was only just why can't you say, according to this simple answer, that by "knowing about Him" the person is just putting other things that exist together to form a "Super Creator".

As I was just writing this, I realized I actually answered my own question that the proof G-d exists is because we know about the G-dly energy behind the worlds, as said above ,or even if someone hasn't reached that stage, he at least knows about the basic energy that gives life to everything, it's simple that everything (or at least) somethings have energy at least giving them life, and because we know about that, that's proof that it exists. So basically, I (with Double AA's help) actually answered my own question.

Answer 1

Ok I realized the answer to the question, after Double AA helped me by asking "What do we know about G-d?", 'cause that is actually the answer.

Basically, this story was told by the Rabbi in context of explaining that there are some parts of G-d that we can know about, like how He gives life to every living being, and (this one takes a little deeper meditation to realize, but still possible to realize that) He creates everything from something to nothing etc.

Basically, this level of G-d that we can know (says the same Rabbi I heard this whole thing from) is on the level of "existence", it exists in at least somewhat tangible terms, and only something that exists we can know about, and only something that we know about exists (as mentioned in the actually story), but there's another aspect of G-d that we don't know about, and that's the part of Him which is removed / separate so to speak from the world(s), that level of Him doesn't actively create the worlds, it's a thing for itself, and regarding that level, we don't know about it, as Double AA said, but the Alter Rebbe's entire proof was just regarding the aspect of G-d that we do know about , namely, the aspect of Him which creates the worlds, since the Alter Rebbe wasn't trying to get into any deep Kabbalah with the Russian, he was just trying to explain simple how we know there is some kind of a "G-d".

So it turns out that Alter Rebbe's proof is only for the part of G-d that we can know about, and the proof is (I guess, someone correct me if they think differently) that since everyone knows about the G-dly life force that's within everything (or at least the concept of life force just for basic, living creatures, since it's obvious that at least some things have life force), so then it must exist, since we know about it, because it's so obvious (I think I'm getting this right, someone let me know if there's any kind of flaw in this understanding of it)