The population won't grow infinitely. People have in average two surviving children when mortality rate is high. If mortality decreases thanks to higher living standards, there is a population boom because more than two children survive. Birth rate then decrease to about two children per woman and population stabilizes. You can argue on why this happens, but this is just observation from Europe to Africa, from the Americas to Asia.
https://en.wikipedia.org/wiki/Demographic_transition?wprov=sfla1




In Belgium, we had a pretty based children TV show called "Blabla". In the opening song there is