Why would it be indefinite? People less likely to have kids exit the gene pool, and a smaller population of those more likely to have kids survive. In the smaller population land is cheaper, less crowded, there are more natural resources per person, and population grows again, from the lower level. Unless you try to short-circuit that adjustment process by keeping the human/land ratio where it is and importing people to keep land more expensive. And then you have to deal with all the costs of ethnic conflict.

China, with a population of 500 million, would be a much more pleasant place to live. China with a population of 500 million Han and 800 million-strong hodge-podge of other groups constantly resenting each other and together resenting the Han? Not so nice.

Things are never monotonically increasing or decreasing forever, and there is no reason to prevent population from adjusting up or down in order to reach better conditions for a given environment. Nor do we need to set public policy to focus solely on maximizing total GDP and real estate values.

My point is if you're concerned about an existential crisis then worrying about the birth rate in one specific country doesn't really make any logical sense. Global warming is a global problem and nationalistic thinking is not how this problem is going to get solved. Getting atmospheric CO2 concentration down to a safe level is going to require transnational cooperation and coordination. Countries with sensible immigration policies and support programs are going to fare better than the ones that lock up their borders (as is now being evidenced in Britain with their empty gas stations and store shelves because there aren't enough truck drivers to deliver fuel and food to all those gas stations and stores: https://www.nbcnews.com/news/world/after-brexit-thousands-fo...).