I´d argue that the course for dominance had been set at least by 1500, if not earlier, although it did not mature fully until about 150 years later. But the relevant developments all had happened before 1500:
Political landscape: By 1500 a number of reasonably stable European states had evolved that were in competition with each other, but none could dominate or conquer the others. They all were large enough and had reasonably developed institution to build up from there and they needed to keep up with each other.
Education and professionalisation: Not only was there a strong drive for better educated populations, with public education spreading, the education system was also reasonably flexible and practice orientated, providing methodic grounding and useful skills/knowledge along with classical/theological knowledge. Moreover many fields were increasingly professionalised at least at certain levels: The core of army command were professional soldiers/mercenaries, major government officials have a legal education or experience in their field, leaders of major banks and merchants provide their sons with both practical and theoretical training according to their means and needs.
Labor efficiency: Not to the same extent as in the industrial revolution, but the Plague fueled a rise of productivity and a partial shift away from subsistence farming in Europe. There also was a wider adoption of simple machinery and in many regions guild restrictions became more flexible. Even hampered by traditions European craftsmen and manufacturies were starting to pull ahead on a per capita base.
International trade and banking: By 1500 were seen as core parts of a nations wealth. Large trade and banking houses were usually active across a multitude of political entities. European traders generally tried to get a foot into the long-distance carrying trade themselves, not just selling and buying. The banks also provided a large number of services beyond money lending and transfer, like insurance and investment. Their business also was no longer based on personal relationships, but on legal agreements.
Economic policies: Moreover European governments were far more supportive of trade and industry than in other parts of the world: They often supported foreign investments within their realm, accepted self organised trade organisation until it openly clashed with their national interests, actively promoted the use of cash crops and did a lot to increase production of strategic or at least profitable goods by private enterprises.
Shipping: European shipping technology was still in its infancy at this point, but they were looking in the right direction: They wanted long-ranged, reasonably fast, reasonably large, reasonably efficient ships, because they wanted the carrying trade to India/reliable transport to the Americas.
Gunpowder weapons: At this point the European firearms were not that advanced, though the innovations in firearms technology now started to spread from Europe instead of into Europe. More important is that Europe now had developed all basic fields of firearms: field artillery, siege artillery, infantry and cavalry weapons. Different nations are developing doctrines best suiting their respective needs and improving the weapons to match that while also trying to get the cost down because they need to keep up with the neighbors.
Now some nations/regions outside Europe still had advantages in some fields and would continue to do so for decades if not centuries, but were grossly hampered by restrictions in others:
The Mughal empire for instance was the industrial power of its age. But it remained funamentally an agrarian state. For example despite a huge ship building industry left long-range trade almost entirely to outsiders. It also never really managed to form a stable, self-sustaining public administration.
The Ming and later Qing had of course a very well developed bureaucracy and strict educational standards for its staffing. Unfortunately the educational requirements were more geared towards classical eduction than to applied administration or flexibility. Furthermore the disdain for trade and merchants in China (and countries under its direct influence) was far more pronounced and entrenched than it was in most other parts of the world. There were at times active efforts to prevent merchants from amassing too much wealth and merchants were systematically excluded from government positions. Coupled with Imperial China´s approach to diplomacy it is unsurprising that they actively fought Chinese participation in international trade. The main reason China was able to keep up as long as it did was their sizeable population growth. Which in turn was fueled by the government surpressing cash crops in favour of food crops.
The Ottoman Empire in military regards remained easily a rival for European powers into the 18th century, but already in the 15th century struggled to keep up with the change to cash-payed armies. They never really found a solution in between religious restrictions on banking, inflation, price control attempts, feudal structures and the shift of trade routes.
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