Many here probably already know about Zheng He's Treasure Fleet of the 15th century, those massive Ming Chinese ships traversing all the way to East Africa, Arabia, Persia, and back to China. In addition to gathering tribute from Southeast Asian countries and Indian kingdoms, Zheng's fleet also interfered in a war in Sri Lanka (Ceylon) between the Kingdoms of Jaffna and Kotte in 1410. The Ming navy overthrew King Alakeshvara of the Sinhalese ruling house of Kotte as a result.
Fast forward a few decades past the death of the Yongle Emperor, and the Ming naval forays into the Indian Ocean were all aborted, the treasure fleets left to rot or scrapped for wood. China turned inward, keeping only a select few seaports open to periodic trade and tributary relations with Japan, Korea, Vietnam, and Southeast Asia. After a fairly disastrous first start at the beginning of the 16th century (due to the overthrow of the Malacca Sultanate), it took the seafaring Portuguese a long while to gain Ming China's trust, helping them to eradicate Japanese Wokou pirates along their shores and establishing Portugal's colony at Macau. Then came the Spanish, whose trade with Ming China became pivotal with the exchange of Chinese goods like silk for Spanish silver from the Americas. By the end of the Ming Dynasty in the first half of the 17th century, the English and the Dutch also began trade relations, and the Italian Jesuit Matteo Ricci called Beijing his home (where he worked on various treatises with Chinese colleagues).
My question is, before the direct European trade relations and contacts with Ming China, which continued as the Manchu Qing Dynasty supplanted their regime, what if China had continued its power projection into the Indian Ocean? What would have happened if later Portuguese and Spanish explorers ran into situations where China through its navy had already clearly established itself as the hegemonic power over the regions of the Indian Ocean? Would that have dissuaded European powers from the slow process of colonizing the Indian subcontinent and Southeast Asia? What would the world be like today if such regions weren't colonized by European powers?
An argument could be made that, with Africa and the Americas extensively colonized, European powers like Spain and England would have gained enough resources and material wealth to then challenge the later Qing Chinese in the Indian Ocean, but before this they would have perhaps been in no position to challenge the Ming. When the Portuguese overthrew the Malacca Sultanate (in what is now Malaysia) in 1511, without a navy Ming China was powerless to restore the Malaccan sultan to power.