There is no one time in history that we can point to and say that there was a breakthrough in thinking regarding diet and health. We've found diet advice written on Babylonian stone tablets, and certain diseases like gout and scurvy have been known and generally understood to be related to diet for almost as long as we have recorded history.

That food contains the necessary building blocks for a healthy body also comes up in Ancient times, although they obviously didn't know about the specific roles certain chemicals and compounds play in nutrition. The Greek philosopher Anaxagoras (5th century BC) theorized that food contained little bits of hair, flesh, nails, etc., that were then used by the body to create those body parts.

There's actually a passage in the Bible's Book of Daniel that offers an ancient testimonial for a plant-based diet. Basically, Daniel and a few others are brought to Babylon to work for the king, but rather than eat the normal rations and wine they ask for just vegetables and water. Lo and behold, after a while they appear much healthier than the others, so everybody's put on the same diet. By the way, it's interesting to note that "looking better" in this case is looking fatter, not thinner.

So, this link between diet and health has been around for a long time, even if the specifics have been a more recent discovery.