The only generals I can think of who were teenagers were nobility who inherited positions or people like Lafayette who managed to use his nobility to convince Washington to make him an honorary general when he was I believe 19.
Teenagers as a whole weren't respected members of adults society in the pre-modern time, even if they did usually have jobs.
As for Alexander the Great he was probably a general as a teenager, but he falls squarely in the "nobility who inherited positions" camp. So much about Alexander is wrapped up in legends and comes from much later sources that we really have no idea how fantastic a "general" he was as a teenager.
In some pre-modern cultures even though a 14 year-old could work, they couldn't inherit, hold office, fully own property, serve in the military, or even marry (without parental consent).
This applies differently to men and women and even in the same culture it can vary between social classes.
[0] https://www.findagrave.com/memorial/55967860/peter-noel_wyli...
For every "teen" Captain there were like thousands of privates, not to mention farmers, deck hands, apprentices, other workers.
And their offspring are the majority...
That's definitely young, but the average age of a Captain in the US military today is 27, and you can be one as early as 25.
In the future, if the human race manages to extend their lifespan to ~200, then people probably won't be considered 'adults' until their 40s. It's all relative.