The Denisovans & Neandertals showed as much potential as Homo sapiens, but became extinct before they got past a stone age level of civilization.
You neglected to distinguish between the Early Stone Age or
Paleolithic Era, and the Late Stone age or
Neolithic Era. The Neolithic began 12KYA with the Agricultural Revolution--the invention of the twin technologies of farming and animal husbandry.
[BTW: The word "civilization" means "the building of cities." Neither the Denisovans nor the Neanderthals invented that technology. The first cities were built around 9000BCE. In fact the first
permanent settlements for people who were
no longer nomadic hunter-gatherers were built at the start of the Neolithic Era (essentially defining that paradigm shift), when
H. sapiens was the only surviving human species.
It is interesting to note that in addition to the potential for the development of a technological culture, there is also the requirement for evolutionary pressure in that direction.
The
pressure for the discovery of agricultural technology was the
unreliability of the natural food supply. Nomadic hunter-gatherers were at the mercy of the weather. Years of low rainfall occurred rather often (on the average about one year out of ten, IIRC), and during one of these years people
died of starvation. This led inevitably to violent
competition among the various small tribes of humans, for their precious hunting and gathering territory.
In fact, reexamination of ancient fossils with modern instruments has revealed the sad statistic that
more than half of adult Paleolithic humans were killed by violence--more than by all other causes combined!
There was tremendous pressure on these folks to discover or invent
technologies that could make the food supply last through a lean year. I'm sure the brainy members of every tribe spent considerable time pondering this issue--while the brawny members were inventing more powerful weapons. This inevitably led to detailed study of the way the food supply is created in nature, and then experimentation with ways to copy nature: planting of seeds, irrigation, protecting (edible) crops from grazing herbivores, then protecting the (edible) herbivores from the carnivores while learning to keep the herds nearby.
The Mesopotamians figured this out around 10,000BCE. The first cultivated crop was fig trees, the first domesticated animals were probably the goats who were attracted to our garbage piles. The people in India, China, Vietnam, Egypt and several other sites in the Old World got the same idea a bit later. The New World had only recently been populated so they didn't have to fight over food yet, but they eventually cultivated the pepper plant. The Peruvians domesticated the llama, but in North America the largest domesticated animal was the turkey. (You try taming a moose, bison or mountain goat!)
In regions where cattle were domesticated, it didn't take long for people to realize that dairy farming is a much more efficient use of pasture land than beef farming. Most people became lactose-intolerant in childhood, but they discovered the technology of cheese-making--more resource-efficient than eating the cows' meat but not as efficient as drinking their milk. A few lucky individuals manifested
lactase persistence, allowing them to continue drinking milk into adulthood. This was a tremendous advantage--both to the individuals and to their tribe--so they reproduced prolifically and their genes became common. Today there are still vast regions such as northern Europe, where virtually everyone can drink milk, and equally vast places like China where almost no one in the native population can.
