This question must be accompanied by provisos. One particular proviso simplifies the task. Assume that the problem solving used throughout the development of language was of the same kind that has at all times occurred since. In other words, assume that it is valid to use averages over time, at least for the time period under consideration. In 2009 I used ideas relating to statistical mechanics to estimate, on certain assumptions (a language-like call `lexicon' of about 100 calls), that language began between about 141,000 to 154,000 years ago in a couple of articles, Article Lexical growth, entropy and the benefits of networking

and

Article A theory of intelligence: networked problem solving in anima...

). at p. 74. The work in those articles is over 10 years old and there have been developments since. One involves dispersion of phonemic diversity (Atkinson 2011). Are there other approaches?

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