If most kids died before age 5 how did we get so populated today? Your math doesn’t add up.
Prior to widespread vaccination, women gave birth to many children. In my family tree, I can find women who had 13, 14, or 15 children. Women had so many children because they wanted at least one or two to survive to adulthood. It didn't always work; I learned about one family in Williamsburg, VA who lost all of their 19 children to a cholera outbreak.
When vaccines were introduced, people still had the habit of having large families. With the vaccines, most of those kids actually grew up. It took a generation or two to change the mindset about having kids. Instead of having large families, people could have small families and spend their energy on raising their two or three children as well as they could. It was during that shift in thinking about the optimal number of children that we had a population boom.
These days, the birth rate is below the replacement rate. It will probably remain low until the population decreases and people think they need to have larger families.