We haven't had a sustainable farm for 10,000 years. Those super fertile cradles of civilisation we learned about in school history lessons are just that - history,.The more you try to approach sustainable the less the farm produces. This is a bit of a problem in a world with 8 billion people.
That's the problem that remains unsolved for 10,000 years. Even if you reduce the number dramatically in one way or another, under favorable conditions it will start growing again resulting in the same overcrowded world.
A significant increase in efficiency for energy production and food production would both result in population increase. Yes. They do already explain the growth over the past 2 centuries. Whether the methods were "sustainable" is another story, but efficiency dramatically increased at this point in history, and the rest follows.
It's these feedback loops in nature which make me question a lot of proxy science like climatology. If you put 0.000001% more emphasis on one feedback over another you end up with a very different answer. What is actually happening is often hidden in plain sight too, but not seen until with hindsight.
While the population has been increasing over that time, the birth rate has been plummeting. So it is not a social/biological positive feedback response. We are responding with a negative stimulus on population. The more energy and food the more time nations have to spend on education and enablement, which has a tendency to reduce family sizes, empowering women out of being baby factories and housewives [sic].
Population has been increasing primarily because 200 years ago infant mortality was about 85%.