The point of divergence for this universe is November 16 1532, at the Battle of Cajamarca in Peru. In OTL, the Spanish force, which was heavily outnumbered by the Incas, succeeded in ambushing their opponents, and seizing their ruler, Atahualpa. However, in this universe, the Incas suspected the ambush, and so attacked the Spanish immediately, taking their weapons, allowing them an easy victory.
Over the next 50 years, the Inca Empire are driven to adapt to European military defences through a second war with Spain, which they narrowly win. This, and their vast mineral wealth, allows them to dominate world politics, science and exploration for the next four centuries.