Humanity spread across the globe over the course of about 29,000 years, encountering terrain from deserts to tundra to tropical jungle. In each new area, they would have needed to find edible plants to forage, since the start of this expansion predated the earliest developments of agriculture by a good 31 millennia. As a starting point, they might have watched other animals to see what they ate, and then followed suit.
So, from that standpoint, it could in part be argued that without animal testing, we'd still be confined to the African Savannah. ^_~
More seriously, many of the medical and scientific advances in the Renaissance and Industrial Revolution involved experimentation with animals. For example, doctors learned about the function of various organs by literally vivisecting living animals and studying their function hands-on before their subjects inevitably died. Not really something you can get away with doing to a person.
As a specific example, there was a famous discovery in 1780 by Luigi Galvani, who observed that frog legs would twitch if exposed to an electric spark. This led to new understanding in how muscles and nerves worked, and eventually to the field of bioelectromagnetics.
And as a non-medical example, some of the early experiments that led to the discovery and isolation of oxygen involved putting mice or other critters in confined containers and then measuring how the air in the container changed as they suffocated. Comparing these results to the results produced by a lit candle in the same container led to the discovery that respiration and combustion drew on the same source.
There are probably similar examples going all the way back to antiquity, if not prehistory. Mankind has been tied to its animals for thousands of years, and we're incredibly observant, so I'm certain we've been studying and watching and experimenting with and on our animals since the first wolves decided it was easier to live with us than compete against us.