It is clear that you have not even read the Vedas to understand its implications on the world, especially in science. Most of the statistics that you ask have been lost due to them being so old, or deliberately destroyed. But we have the results to prove that these existed. "Strong observations & correlations" are just another way of saying "trial & errors".

Not just ayurveda, but take any science or even Mathematics. The Vedic civilization has been too far ahead of its European counterparts. In fact the idea of heliocentrism, gravity, action=reaction, universe & its age, speed of light, distance of the sun & moon from earth, understanding of time travel, time zones, metallurgy, the so called pythagoras theorem, sudoku & its various forms, the numeral system etc etc all have Indian/Vedic origins, so why would you doubt vedic medical sciences so much? There is also substantial evidence for surgery to have developed in Vedic India far earlier than Hippocrates or any Western counterpart. I firmly believe that if not for the muslim hordes who destroyed everything under the pretext of war, mankind would have been able to make better use of mankind's ancestral knowledge.