We have no idea when exactly Homo started to "talk" language in last 3+ millions of years. Maybe it is as old Homo - maybe even older. Mammals use sounds and even talk - birds can communicate with sounds, also - insects. Besides, language is only part of communication of humans and not least significant part of it is body language, which is also used by all mammals and even other species in tree of life. Bushmen people use click sounds in their language - it is something that IE speakers do not use as very meaningful form of communication, but it still can be used to express what I'm thinking of your proposal that there developed independent Proto-language groups even better than using written words: tsk tsk tsk(accompanied with moving head to the left and right during making tsk tsk tsk).

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If the idea is that people in Africa were mutes or did not use language before spreading out and that all the modern languages have different sources of development of language out of nothing, good luck with proving that... because languages seems to have developed in Homo, before Homo became Homo Sapiens and Homo Neanderthalensis also seems to have been capable of using talk. But if the question is regarding modern languages if they have one origin or are they all more or less related to each other and sprung from one source, then most likely that there was only one source for all modern human languages and that this source probably developed much later than Homo Sapiens diverged from other Homo.