The biggest driver of the shift from large families to small families is communication technology and education. As these techniques come into place the switch to lower birth rates is faster than what demographers have expected. And they are more permament.
Current estimates of the world's peak population are made with assumptions that don't take into account the major role that globalization is having.
This means the earth's population will reach its peak sooner than official forecasts predict and because there is no visible counterforce compelling the majority of couples to have more than 3 kids each, world population will rapidly fall after reaching its peak.
It will diminish to our level by 2060 and keep falling.
Median age of world population is around 30 years. Access to healthcare is improving -> longer life expectancy.
Fertility rates can fall very significantly and your prediction will still be wrong.
I see my (anti)prediction as a bet against a major
catastrophic event (war, economic collapse, dangerous epidemic outbreak etc.) and mass human colonization of Mars.
In 02070, the UN estimate of 02060 World Population will be less than the UN estimate of the 02003 population.