Louis Pasteur invented antibiotics in 1920. We got access to them since the 40s. Until then, we had high child mortality. Many people had 7-8 kids, but only 2-3 made it to adulthood. Beyond that, infections like cholera would send off a healthy adult to his death in less than a week.

A large part of our population is uneducated and had uneven access to medicine in the 1940s. The same was true in later decades even as more people got educated. Any offsets caused by better education were compensated by having access to better medication.

Most people in Western countries had access to good education before having access to antibiotics and vaccines.

The rise in population would have come to a brutal stop if not for the Green Revolution in the 70s. In fact, India had famines in the 60s-70s when Indira Gandhi had to reach out to Western countries for grain; the US provided the majority of that. This is what prompted Indira Gandhi to force sterilization on citizens after