There are currently about 5000 languages spoken in the world, and a third of them are in Africa. Human language probably originated there, and relatively few languages were 'exported' to other continents.

Small clusters of hunter-gatherers would have been able to invent simple language, but not sophisticated language with grammar and syntax. There must have been one or more densely populated places in Africa, where people were actively engaged in talking. But there is no fossil evidence for such a large concentrated population. I think that is because the people were on beaches, which are now submerged.

If a beach area had a large and reliable food supply, hundreds of people could live on the sand or in the water. And what do modern beach-goers do all day? They talk, and listen to words and songs. That's how I think human language first evolved.  

It is said that societal evolution went through 5 stages: 1. Hunting/gathering, 2. Horticultural/pastoral, 3. Agricultural, 4. Industrial, 5. Postindustrial. 
But I think human language suggests there was an earlier stage: 0. Early-human discourse.

I think the first people were crowded tightly together in the water near large beaches, talking and singing most of the day using a proto-human language. It was an easy life, and they freely shared their food (sea-turtle meat and seaweed), genes, thoughts, and feelings throughout the large semiaquatic crowd. Their main activity was talking and singing for entertainment and for status. Stage 0 could be called Talking heads, since peoples' heads were sticking up above the water.

When outcasts and explorers successfully migrated to more dangerous and difficult places on the mainland, they invented clothing, weapons, and fire. They became (1.) Hunter/gatherers and then (2.) Horticulturals/pastorals in new lands. Each small group began with the proto-human language with its sophisticated grammar, and then added new vocabularies, evolving new languages.

Talking was still valued in the new languages -- not only what was said, but how it was said.