Contrary to popular belief (Indiana Jones), archaeologists at academic level are incredibly specialised. They will purse an avenue of specialisation fairly early on in education (pottery, metallurgy, landscape, art, generalised region, etc.). The identification of human remains is something that is conducted by an archaeologist with years of experience and often extensive cross-training, though medical professionals such as pathologist can learn this skill set and often moonlight.

The skeleton has many identifying markers to tell age. Milk teeth being present, unfused bones of the skull (children), size of bones, development in bones that only occur at certain ages (fusion of bones), degenerative changes from use (arthritis). When looking at remains they are looking at the whole picture.

It is not a precise science, as they cannot tell the exact age by just looking at the bones but they can give a relatively close range. Also, keep in mind that archaeologists often do not work with a whole skeleton. Parts get crush, exposed, lost, or even treated in ritual, are all factors that require some knowledge of the culture and time. This is why grave goods, items found around the burial site, are very important.

The bones also can give away indicators of status, profession, disease, and general health. A famous study found archers had more muscle attachment points in the forearms and shoulders. Hoplites should similar developments from carrying heavy armour and hours of training with a spear. On the domestic side, remains have been found that had spinal issues and evidence of hours spent kneeling on bent toes — the effect of hours knelt cooking. Skulls can be found with holes, pointing to trepanation, which can narrow down to a time period. Skulls can also be found with the ravages of syphilis, leaving dozens of pinholes in the bone.

So while teeth are great, archaeology is piecing together what you can find and often what you cannot.