The only way you could know (prove) that it worked would be to go back in time and go throught the same time period again without the treatment and compare the outcomes, other wise we have anecdotal singular evidence which, when taken together with lots of other singular events can seem to provide a credible body of evidence that a process or intervention works.
Given that it is not possible to time travel as far as i know then the next best thing is to provide the treament to as large a number of people as possible with a similarly large group as control with no intervention.
Comparing these group outcomes will indicate with some level of certainty whether an intervention was effective or not unlike singular events.
For example the oldest recorded woman was a lady by the name of Jeanne Louise Calment who dies at the age of 122. She smoked all her life (well gave up at 119 cos she couldn’t see well enough to light up) and ate a minimum of 2lbs of chocolate per week.
Hence on a sample of one we can show that eating excessive amounts of chocolate and smoking is very healthy and will help you live to a great age.
WTF?
It helped – of that I’ve no doubt. I’m not obliged to prove anything.
I’m off to the pub to watch the rugby.