In 1492, The Ottoman Sultan Bayezid II sends out two large fleets in "pursuit" of Christopher Columbus.
They land in what would have become the island nations of Haiti/Dominican Republic in OTL, and founded a town, naming it 'New Istanbul", after which the island territory is named for. The second fleet re-supplies and refits, and lands on the coast of Mexico.
Aztec War (1492-1499)
The Sultan 'conquistadors' fight a seven year long war against the Aztecs, ending the war with the Treaty of New Istanbul, which sets up peace between the forces, secures trade, and makes the Aztec empire an ally of the Ottoman Empire. This prevents the Spanish from conquering Mexico.
The Ottoman's then use the Gulf territory, (henceforth named the Sultanate Gulf) to launch an invasion of Northern Brazil.
Alliance with the Hapsburgs & results
The Sultans forge a tenuos alliance with the Hapsburg dynasty in Austria, which cements their foothold in the Balkans and Greece, while securing peace with the Austrian Empire.