I would attribute more of the decrease in child mortality to clean water and better nutrition. Vaccines played a negligible roll (diseases were already well past their peak when vaccines came out).

Clean water and better nutrition are direct results of scientific findings...

Clean water has become more consistent, but it was common in many areas historically. You see remnants of this for example NYC is exempted from water filtration requirements due to how clean their water source is.

Good nutrition was similarly common in many areas historically even without scientific understanding of nutrition.

The reason clean water became consistent is because science told us clean water is important and how to make clean water widely available. Nutrition became better because science allowed us to grow more food across more land more easily. Things like crop rotation, mechanization and fertilizers allowed less land to feed more people a better diet.

> The reason clean water became consistent is because science told us clean water is important and how to make clean water widely available.

Both of these long pre-date according resembling the scientific method of germ theory. We’ve known that dirty water makes you sick and how to filter it for so long that the first example of a functioning sewer system I know of is prehistoric[1]. And clean water was transported over hundreds of miles through Roman aqueducts. They didn’t do that for no reason.

[1] Mohenji-Daro https://indusrivervalleytechnology.weebly.com/the-sewer-syst....

The Roman water system also included lead pipes which poisoned its citizens. Victorian London included elaborate systems to pump water that was 'clean' inasmuch as it didn't smell like the Thames, but it still killed hundreds of people before Jon Snow searched for evidence to support his contested theory that the cholera outbreak could be traced to use of a particular water point

There's a big difference between water that is nice to drink and water that doesn't contain harmful pathogens, and cities that had piped water for centuries stopped killing their inhabitants from water-borne infections when scientists figured out germs existed and could be killed

That cholera outbreak was notable because most of the city had clean drinking water. Which means their mitigation strategies largely worked even as they didn’t understand the root causes of cholera.

Also, Roman aqueduct water had minimal lead contamination due to the high flow rate, unfortunately they used lead for a huge range of different things like cups which got lead onto people’s mouth and hands while eating etc.

"We" also believed that cholera was caused by miasma, not dirty water. It was science that got everyone on the page that clean water was important to prevent disease.

Are you aware that vaccines came out way over 200 years ago in Europe? And the technique was known for quite a bit longer in Asia: https://en.wikipedia.org/wiki/Inoculation#Origins