1. Swahili City States unify as a East African trading empire before the Portuguese show up, get guns and cannons from the Ottomans, and successfully keep Europeans out of the Indian Ocean trade network for at least until the 1600s. They then colonize coastal Madagascar, Comoros, Mauritius, the Seychelles, and other islands in the Western Indian Ocean, as well as settling slightly further into the African mainland.
2. Mongol Empire decides to mass produce opium, marijuana, and use their control of the Silk Road to sell these addictive drugs as medicine to Europe's nobility during the Black Plague, thus getting Europe's most educated people into becoming drug addicts which slowly then descends into the European merchant class as well, leading to the Mongols becoming the world's largest drug cartel and preventing Europe from rising to prominence due to being stoned out of its mind.
3. Romans did send expeditions into Sub Saharan Africa. Perhaps after invading the Garamantes in the 1st century AD, a glory seeking Roman general sends his legion to Lake Chad and conquers the area. Then due to political intrigue, the legion becomes labeled as traitors, another Roman legions destroys the wells in the Garamantes cities (which required heavy maintenance to maintain), and the Roman legion in Africa becomes forever cut off from Rome, forced to build its own blended Roman-African civilization.
4. Vikings sailing down the coast of west Africa and turning the Canaries and Cape Verde islands into Viking Kingdoms. These then start off raiding as slavers but eventually develop plantation economies that trade with Europe but also begin adventuring further down the coast of Africa.
5. Surviving , yet highly autonomous Viceroyalty of Peru (which almost happened) which becomes of the most powerful and wealth South American country (although its more of a vassal). It then becomes the first power to colonize much of Polynesia as well and reconquers Chile.