I assume you're talking about Alexander Hamilton. He never rose past the rank of colonel. He did use connections to form a militia of college students that he led as captain. I believe he was either 18 or 20 at the time (there's a debate over when he was actually born). And he was later elevated to a colonel in the continental army, but he wasn't a teenager when that happened.
I thought that could be the case, but since I'd mentioned Washington and Lafayette I leaned towards Hamilton being the intended reference.
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.
I would think that children might be some of the best military leaders, since they'll have no preconceptions about how a war must be fought, but will take the most direct route to victory.