The Third Age of Mankind
officially begain in the Babylon 5
episode Into the Fire
, when Lorien, the Shadows, and the Vorlons departed for the rim along with the other First Ones
The Third Age of Mankind is not a reference to humans only, instead it is in reference to every space-faring species in the galaxy at the time.
With the dawn of the Third Age of Mankind, humans among every other species had the gaalaxy to themsleves for the first time. There were no giants in the playground for the first time in the memory of those species; there were no parental-figures to look up to, seek advice from, and obey.
In the Third Age of Mankind, the sentient species of the galaxy were fully in control of their own fates for the first time.