Quick answers to the question, how does human being emerge from the state of nature for Rousseau.
1. Society, language and reason are concomitant activities/states, mutually conditioning and enabling. This means that in society (by which I mean simply human cohabitation) humans have need of language, and without this need they would not develop it. Without language humans could not develop reason, which itself represents a late moment in the development of language, from its initially simply nominal function to a later metaphorical/abstract capacity. Lastly, without reason they would not have the foresight necessary to establish different occupations and the division of labor that makes cooperation desirable (beyond the occasional intersection of interests nullified when those interests are satisfied).
2. Therefore, neither society, nor language, nor reason could be the cause for the exit from the state of nature, because they are as equally products as is the civilized man.
3. If it were the case that humans emerged from nature because of their capacity for thought, then this would negate one of ways that Rousseau wants to distinguish himself from the Western philosophical tradition in his claim that anthropological difference is the result of freedom and perfectibility, not ratio.
4. I surmise that Rousseau thinks that it is truly a piece of historical contingency that caused humans to enter the cohabitation that makes society, language and reason possible. Some kind of environmental event along the lines of a volcano or earthquake.