For what it's worth, the conversation so far has seemed to conflate the "teaching assistant" with the "associate". The teaching assistant (or TA in my neck of the woods) can be any graduate student, from their first day in grad school. They are not in charge of a course, but are given assignments by the course instructor to do administration or potentially run a smaller section of class.

The teaching associate, on the other hand, teaches their own course with very little oversight. They are responsible for course content and evaluation, and might have their OWN TA's. It's a very different experience, and (again, at my school) only available to grad students who have passed their written and oral qualifying exams after their second year.