That's the point of the whole "...called the Third Age by some..." intro to the books. Their timeline is not a straight line - it may very well be the case in this universe that the seeds of the beginnings of certain elements of Ages to come are planted in small amounts in the past, so each succession of Ages build on one another.

In other words, there is no "beginning", but there are "beginnings". Hence, there is no FIRST Age, but there are Ages that are called "the First".