The Mezzanine

IIRC Kendra said (or strongly implied) that her family had been involved with the Council for some time. So I've always thought that while the Council may track hundreds of Potentials. they probably have a much smaller number of Potentials who are considered most likely candidates to become Slayers - either because the signs and portents are favorable, or because they come from families with a history of turning out Slayers, or something. And it's those girls who get the Watcher from the age of two. The vast majority of Potentials, like Faith and Buffy, aren't given any sort of special training, and may never know who and what they are.