There’s no definite information about what year he was born, but his physical body died in 3996 BBY. We can safely assume that he was an adult here. Considering the fact that Jedi are trained at a very young age and Exar never fully completed his Jedi training, he would have become the Dark Lord of the Sith at a fairly young age compared to many other Dark Lords. His spirit lived for another 4000 years trapped on Yavin 4. This is what I love about Exar Kun. He has interactions with both the Old Republic characters and the Jedi underneath Luke Skywalker.