I think we first have to ask what we mean when we say that the Europeans “dominate[d] oceans.” You describe this as something that “becomes more obvious after the fifteenth century,” when Europe began colonizing and conquering.
However, Europeans did not in any sense dominate the Pacific at this time; the Polynesians colonized New Zealand about two centuries before the start of that period, and had already colonized as far east as Hawaii and Easter Island. Nor did they dominate the Indian Ocean, which was why the Portuguese felt they needed to conquer Goa and Malacca to be able to claim a piece of the thriving maritime trade. Nor were Europeans in control of even the Mediterranean until an alliance of Catholic powers defeated the Ottoman Empire at the Battle of Lepanto in 1571. And I think you would have a very difficult time convincing anyone in China that Europe already dominated the oceans at the time of Zheng He’s voyages.
So what it sounds like you really mean is, why was it European armies that landed on other continents first and conquered the inhabitants?
One factor is certainly geography. As previously mentioned, the Polynesians got as far as Hawaii and Easter Island, but from Easter Island to the mainland is more than 3,500 km with no other habitable islands in between. Easter Island itself only supported around a few thousand people and doesn’t happen to have a large iron mine, so it’s impossible to imagine a huge army of Rapa Nui forging iron weapons and sailing off to conquer the Incas, even if they hadn’t made the mistake of cutting down all the trees. The Bering Strait is much narrower, and people did cross it by land in prehistoric times and settle America, but it would have taken more advanced ships to reach the Americas by sailing east from China than west from Europe, because the distances are greater and the prevailing winds blow the wrong way.
Jared Diamond, in his book Guns, Germs and Steel, argued that there was a good reason: in his theory, the climate and trade zone spanning most of Europe, Asia and North Africa is by far the largest in the world, and also contains all the natural resources it needs, such as copper and tin to make bronze, while the other regions of the world are separated into smaller regions, or were too cold to support a large population, or were too hot and held back by tropical diseases. Then, prehistoric humans killed off most of the megafauna, and most of the domesticated species that were left were within the Europe-Asia-North African zone, spreading within it long before they spread beyond it. Not only animals spread across this region but not beyond it, but ideas, and inventions such as gunpowder.
Diamond argues that most human diseases start out as animal diseases, so this also meant people in this region caught more diseases. This was, counterintuitively, a great advantage: when people from other continents, with many fewer kinds of domesticated animals to give them new diseases and fewer populations sharing diseases with each other, first came into contact with Europeans, the Europeans were carrying vastly more deadly diseases to which the people they met had no immunity, and as a result 90–95% of the Native American population died to disease without European armies needing to fire a shot.
There is definitely some truth to this. The Vikings brought cattle with them to their colony in Greenland, but their herds were unable to thrive there because the climate was too different. The prehistoric relatives of horses went extinct in North America at least 11,000 years ago, there was never anything like it in Australia, and no one ever domesticated the moose or zebra, so no natives of those regions could have had horses or anything like them at the time of contact. Any civilization would have had huge problems when the the vast majority of its population died to disease immediately before foreigners invaded.
This theory, though, does not imply that Europe had any geographic advantage over Asia and North Africa. Diamond suggests that Christianity was especially willing to endorse military expansion, but even a cursory look at the history of other empires suggests that it’s far from unique in that regard. Why didn’t the Mongol Empire, when it controlled East Asia, put the largest and most advanced army in the world on a fleet two centuries before Columbus, arm it with gunpowder weapons from China, and sail across the Pacific to conquer Japan? Well, they did, twice, but their fleets were hit by typhoons and they gave up on that plan. (What would Spain have done if both Pizarro and Cortés’ expeditions had been total losses?) Diamond himself fell back on the same explanation as the other answer: Chinese court politics ended its Age of Discovery, and since that became the policy all over China, its naval tradition died out. When Christopher Columbus couldn’t convince his own small country to fund his idea of sailing west to India instead, he kept trying others until the Queen of Castile said yes. His plan did not make a lot of sense (Even in 1491, educated Europeans knew that the world was larger than he thought and Asia was narrower, so it would not have been a shorter voyage and the ships of the time would not have been able to make it even if America had not been in the way. And many historians now believe that Portugal had already discovered South America by then, but were keeping it a secret so that no one else but them could exploit it.) but all it took was one independent monarch to say yes, and someone in Europe tried the long shot.
Stephen J. Gould’s response to that was to ask: in the world where China colonized America, wouldn’t we be saying, of course it was inevitable? All the European countries were so much smaller and poorer than China and preoccupied fighting each other, or throwing their resources away on pointless crusades. Of course a country like Spain could never have conquered the New World before China got there! Diamond’s response was basically to say that that Gould was focusing on the weakest part of his argument. And you would also need ad hoc explanations for why Morocco didn’t do it instead, or Siam, or Japan.
Unless we someday discover a parallel Earth with a different history, we’re not going to get a chance to re-roll the dice. Portugal was lucky to have a ruler at the start of the 1400s who gambled on the potential of sea power, and then everyone else in Europe heard about it before the rest of the world and raced to catch up. But maybe it could have been a sultan of Morocco, or a shogun of Japan. Or maybe other factors already guaranteed by then that Europe would put together the weapons, ships and belief system that conquered the world before anyone else.