It seems there are a lot of theories about how humanity escaped the Malthusian Trap, defined as such:
The Malthusian trap, named after political economist Thomas Robert Malthus, suggests that for most of human history, income was largely stagnant because technological advances and discoveries only resulted in more people, rather than improvements in the standard of living. It is only with the onset of the Industrial Revolution in about 1800 that the income per person dramatically increased in some countries, and they broke out of the Trap
That is: more total wealth led to more people, and the per capital wealth remained unchanged. I'm sure lots of historians and economists have covered this ground before, but the explanation for how humanity escaped this trap seems pretty obvious to me.
At some point in history, wealth started being generated more quickly than humans were generated. The percentage growth of wealth may have remained the same, but the absolute value of that growth kept increasing. At some point, the absolute value of the wealth increase was more than could be absorbed by simply having more kids. The "wealth/person" ratio had stayed constant, but at some point the numerator started growing faster than the denominator could, due to biology.