As others have pointed out, he could not be younger than about 3800 years, and is likely much, much older.
The real question for answering this question isn't "How much time since since the veil was put up," because we know roughly when the veil (3874 years ago) was put up and we can calculate from there. The real question "When - and was - Solas born in an age when elves were immortal?" Because that could be any time.
One curious comment of his about the evanuris - and he was one of them - was "The first of my people do not die so easily." "First" could mean most powerful, but it could also mean "firstborn." It's entirely possible Solas was one of the first elves in existence. And if elves started as spirits (the most popular theory) then his beginning is with the beginning of those.
All this is assuming the existence of time as we know it in a pre-Veil world. Every time that time and the Veil comes up, things get muddy - such as in "In Hushed Whispers" when twists in the veil can alter time, or "Champions of the Just" when hours of Veil time passes in instants in the real world.
It's quite possible that before the Veil, there's simply no way to express how old he is.