I come into the world where other beings are using language. I learn this.
Those beings have come into the world where other beings are using language. They learn it.
Those other beings come into the world, etc.
This is not an infinite regress, as we go down the chain of being, we come down to plants and they commonly are taken not to have language.
Is then language 'private excreta', rather like the coral reef, where the organisms subsist on the excreta of the old.
Wittgenstein famously argues that there can be no private language; that language, in order to be language, must be (at least theoretically) public. I've not come across a convincing refutation.
There have been a number of philosophers (such as Rousseau) who have written (speculatively) on the origin of language, although this field is more currently the domain of anthropologists and biologists.
One of the complicating factors, from a philosophical perspective, is determining the limits of "communication" and "language" in this context; for example, one could argue that a flower is indeed sending a message of sorts to a bee, by means of color markings and scents.
What Wittgenstein means is that there is no language which is necessarily private.
You could keep the language a secret but this is not the same as necessarily private. The secret language still has to correlate with objects in the world and this can be deciphered. Furthermore the language can be taught by the secret linguist.
Language can not be necessarily private because language is communication which is public. The idea of a private language is contradictory and mistaken.
Most of what Wittgenstein wrote in Philosophical Investigations can only be understood in the context of some specific argument or question he was writing about or talking through at the time. I do not think any of the statements in PI are intended to stand alone. I suggest that if, for example, W wrote in PI, or other work of that period, that language must be public, he did not ever intend such a statement to be a fully established eternal truth, nor even a postulate, but merely a sort of signpost to help a reader follow a particular path in a particular forest that he was constructing in his imagination and trying to make visible and traversable in the mind of a reader or listener. In that way, over time, W was able to teach by example some patterns of thinking which he had found useful.
Wittgenstein was not arguing against the type of language you are talking about in his private language arguments. At length in various notebooks, Wittgenstein wrote about various possible people who speak a language without a social setting. He discusses Robinson Cruesoe in his notebooks and is completely ok with the idea of Robinson Cruesoe living by himself and using words, or coming up with his own language to describe how he goes about his daily tasks. What is important to Wittgenstein is for it to be a language, it must be in principle possible for you to observe him or interact with him, and get a sense of what he means. For example, maybe he leaves signs on the ground to help him remember where to find various natural resources, or to help him remember melodies of songs he writes, etc.
Wittgenstein is also not trying to put forward the argument that language has to be learned in a community. He discussed the possibility (again in his notebooks) of Martians who are born with an innate ability to speak. He doesn't believe that that is impossible or incoherent. How the person comes to develop language is not important. What he is arguing against is the possibility of a language which is necessarily private, ie not reducible in principle to any public notions. For example, someone who tries to privately ostensively define certain sensations he or she has. Or philosophers who claim that language is essentially private (ie the definition of pain is that private sensation you have, which leads to people saying things like ("I don't know if other people's pain is real, as I only know with certainty that my pain is real").
EDIT: Check out the Analytical commentaries on the Philosophical Investigations by PMS Hacker if you really want to delve deeper into some of exegesis of PI. The idea of Robinson Cruesoe, the Martians, etc, is discussed at length
