Every now and again similar questions come up in HubPages as well as other venues. My answer is always the same. True, I may be deviating somewhat from the scope of your question as my answer actually falls back into what would commonly be referred to as prehistory, but my answer to the biggest event in human existence is the discovery of the ability to control and to make fire.
Dating back probably to homo erectus, one of the hominid species that immediately predated modern homo sapien, that ability to control fire and to pass that knowledge down to future generations was the birth of technology. It spawned the ability to mold our world to our convenience and advantage. It placed us on the top of the food chain for good.
That, to me, is the biggest event ever as far as humans are concerned.