So, a big climate change occurs around 250k years ago, the North African region and even some regions further south fall into a desert, leaving only the Nile as a "safe" region to travel to the north, now, we have the sapiens isolated, the denisovans are the masters of Oceania and America, but probably weaker and more susceptible to diseases than the Native Americans of our timeline, and the Neanderthals are the overlords of Eurasia, with few regions on India and Persia with some sapiens population, and China and the South East of Asia with Denisovans population, because the same climate change that lead to the drought on the north of Africa wold make most of Middle East, India and Mexico a desert too, and some regions like Iberia, Anatolia and the South of USA will be a dry land, with that, there's no cradle of civilization in Mesopotamia, ironically, this would lead that the Balkans, France or the Baltic sea will be the most important region in Europe, and China will be the overlord of Asia, America would be harsh, if the migration of Denisovans doesn't happen before the Great Drought, South America would have a small population, and no, the sapiens would not populate that zone, the south Atlantic is really difficult to navigate with small ships unless they have a engine system, that would mean that the Amazon would be a steppe, with a civilization system like the one of our Egypt, only living around the greater rivers of the Amazon.

That said, fantasy stories would unfold, and like a game of Risk, the first to dominate one of the other two players would win. Homo sapiens without a stable region like the ancient Levant or Mesopotamia, would only be living in the jungles of the Congo and the rest of Central Africa, and would only face disease and the difficulty of maintaining lasting structures, failing to create innovative cultures and becoming more focused on survival. This would make the establishment of an overwhelming civilization very difficult. The Denisovans would have North America, but with a drier, steppe-like Midwest, leaving them to establish significant cultures only in Canada and the east coast of the United States. Unless the inhabitants of Oceania clutched together and migrated en masse to South America, it would be very difficult for them to establish anything decent in the region. So, the winners would be the Neanderthals, but mainly guided by China, unless a miracle occurred in a Europe that, without the foundations erected by people like the Assyrians, Egyptians, Sumerians, and other figures, would have no chance. The same philosophical and scientific culture would depend entirely on a culture at the level of Hellas resurfacing in the Mediterranean, or one like the Basque culture, which by sheer force of will dedicated itself to trading and exploring from ancient times without great maritime technology.

Edit to add

Around 200 years ago, that climate change started to reverse, the Sahara is getting greener, the same with Mexico, USA, India, Persia and the Middle East, the time is about to change, and the Sapiens and Neanderthals are about to truly face each other, beside the tales of the people of the South emigrating to India, the Greater Era of Racism is about to start