Humans and Neanderthals had a common ancestor about 400,000 BCE (current estimates range from 320,000 to 800,000 BCE). Humans did not evolve from Neanderthals, but both are the current evolution of a common ancestor tentatively identified as Homo Heidelbergensis. After the split, Homo Sapiens and Neanderthals interbred up to and as recently as 40,000 BCE. Through DNA testing we can identify DNA that came from interbreeding with Neanderthals. Neanderthals became extinct about 40,000 BCE. They built shelters, wore clothes, used tools, and spoke. We know that about .03% to 4% of the genes in non-African modern humans is from Neanderthals. Neanderthal DNA in modern humans is the highest in East Asians, intermediate in Europeans, and lower in Southeast Asians.
The common ancestor tentatively identified as Homo Heidelbergensis lived from about 600,000 to 200,000 BCE. The 400,000 BCE documented here is just a reasonable guess.