I can really only answer definitively for India, but I imagine it is similar elsewhere. In ancient India, they kept their teeth clean with sticks, typically from neem or babul, that they used to chew, brush, and pick their teeth with. In fact, many if not most Indians still use chew sticks today called datun.

Essentially, you take a twig from a tree, peel the bark from one end, chew it a little, then brush. It is an ancient but effective method that works surprisingly well.

Since trees decay fairly quickly we can only guess for how long this has been used in India, but our earliest record comes from a surprising source, the Sutta Pitaka. AN 5.021 (Pāli) and the corresponding EA 36.3 (Taishō) detail why using dantakattha (Pāli for "tooth cleaner") is beneficial. Being present in both the Āgamas and the Nikāyas and having older language, it is clearly from the early stage of sutra literature, so at least the 4th century BC probably older.

Here’s an answer by /u/Aerandir about this question from the FAQ list.