Really? Because one obvious thing it'll require is about a doubling of the birth rate ... it's not about growth, it's about stability. At least at first.
Population stability and economic/societal stability don't have to be the same thing.
If someone cracks the "robots that can do human-like things" boundaries in the real world versus just text - and there are enormous efforts in this regard going on - I'd fully expect some tasks to be handled by non-human workers.
It seems a lot more likely than "number goes up" next-quarterism driven economies are to survive a thousand years.