The word 'being' can mean 'creature' or 'as' (i.e: 'being / as a rich man'). What is the meaning of 'non-been Being' exactly? . Is this ambiguous?
Experimenting with a new language is a great way to learn. Sometimes you discover for yourself how people express their ideas in the language and sometimes you find bizarre constructions that no fluent speaker would ever say. In this case, you've found a bizarre construction that appears meaningless to fluent speakers.
"Being" as a noun
The sense of being that is a synonym for "creature" is the present participle of "be", used as a noun. The idea is that a creature is something that "is", i.e. something that "is being"; and a special sense has developed where calling a creature (or person) a "being" emphasizes something distinctive about it, as in "a rational being", or that the creature is unique or strange, as in "a being from outer space".
The word been is the past participle of "be". Past participles in English work either as adjectives that modify a noun, as in "a torn jacket" or as the main verb in a perfect tense or the passive voice, as in "Mary has torn two jackets this week" or "This jacket was torn by Mary." Your phrase uses "been" as an an adjective modifying the noun "being", so let's look more closely at that.
When a past participle modifies a noun, its meaning is usually passive: it means that the noun was the object of a past action of a transitive verb, as in "a torn jacket" (someone previously tore the jacket) or "a stolen wallet" (someone previously stole the wallet). Since "be" is intransitive, "been" can't work like those verbs. We can't hear "been" in "a been jacket" as denoting a past action upon the jacket.
There is also a less common way that past participles work as adjectives, where the verb's meaning is active: to mean that the action of the verb, with the modified noun as subject, has happened in the past. For example, "a grown man" is a man who has grown (to adulthood); "an experienced politician" is a politician who has experienced (a lot of political activity). This is the only way I can make sense of "a been jacket": to mean a jacket that has existed. But this is a very odd construction—so odd that it does not seem to have any clear meaning. Perhaps "a non-been jacket" would be a jacket that has not existed—but this construction is even more bizarre.
The main use of been is to form perfect tenses with other verbs:
Mary, have you been tearing jackets again?
This jacket is brand new. It has never been torn.
There are a few special senses of been, though, that work differently:
Have you ever been to Hawaii? (That is, have you ever traveled to Hawaii? This sense of "been" only exists in the past participle and future tense; it has no present tense.)
Before he appeared in the movie Pulp Fiction, the actor John Travolta was considered a has-been. (A "has-been" is someone who used to be famous but is no longer considered important even though they are still alive.)
"Being" as "as"
The sense of "being" that you saw defined as "as" is really just the present participle of "be", used in a sentence like this:
Being a rich man, Tevye can afford to buy fancy clothes for his wife Golde.
Tevye, being a rich man, can afford to buy fancy clothes for his wife Golde.
These mean the same as "Since Tevye is a rich man, he can afford to buy…"
I hope that explains why fluent speakers find "a non-been being" nearly incomprehensible—and also shows you a little more of how been and being normally combine meaningfully with other words.