The estimated time when the multiple languages started from the original single language is found in the Tower of Babel write-p in the Book of Genesis/Bible. This is around 2240 BC.
Just about a hundred years before this @ 2350 BC, the earth had seen a worldwide flood and the memory of this would be fresh in the memories of the population that began to multiply again from the 8 of Noah's family. About 100 years after the Flood, people again seemed to have forgotten the instructions given to them to 'be fruitful and multiply, and replenish the earth'. Perhaps they became fearful to move around all over the land areas, and stuck together in one place and built the tower to reach the heaven. Maybe a fear of another flood caused them to forget God's protection. It doesn't take long for man to make wrong choices. They did build up to about 91 meters and then God confused them in creating multiple languages, wherein the workers were no longer able to understand each other much, and the work on the tower ended. People banded together with same language speakers and forced to move on to other places.
That is a brief idea of how languages came about. God created the languages.
Thankfully it wouldn't have taken millions of years for languages to evolve, knowing the life span of man was fast decreasing from 900+ years before the Flood to around 70 in a few generations.
If one looks at the origin of languages with documented proof from stone writings and other materials, they point to a time around 2000 BC. A quick search on the origin time of a few old languages points towards the same time period as of the Biblical account of the Tower of Babel.
Not sure of other languages that talk about the Tower of Babel, Flood and Creation, but it is clearly seen in the Chinese language characters. Again, the Chinese history starts around the same time as the end of the Tower of Babel.