It's more complicated than that.
Before the Printing Revolution (Guthenberg's invention) and the Age of Explorations,
China was the epicenter of science, trade and world-dominance in terms of GDP produced.
While the Islamic Civilizations were quite dynamic up until the 13rd century, the Ottomans by their genius tactics became the new Hegemons of the Muslim World, but unfortunately for them, after the Fall of Constantinople, many Christian Orthodox left with them the Ancients' wisdom, thus marking the birth of a new Era; the Renaissance.
Long story short: despite the hegemony of the Turks in the control of the seas, the Europeans learned the existence of a new continent, later named after an Italian Explorer; Amerigo Vespuci.
During this time, many pilgrims left the "Old Continent" (Europe), fleeing from persecutions and famines, for a better life. In this prism, European genius started.
They quickly improved many formely Chinese inventions; gun powder, maps, etc.
While, in the South of the Hemisphere, the Muslim World was stagnant; Egypt and Iraq weren't producing enough intellectuals to compete with the Europeans. The Chinese began, in the 16th Century, to isolate themselves from the World. In Africa, only a few places were "civilized" enough to have records; Mali, Shongai Empires, Abyssinia, Nubia, Kongo, Somali Sultanates, Alawite of Morocco,etc. In South-East Asia, it was around that specific century that we can the expansion of Islam in the Indonesian islands, with many convertions (credits to Indian and Iranian merchants), with the rise of the Aceh Sultanate. Consequently with the appeal of these dynamic regions, they gathered with them many Dutch and Portuguese "merchants", later, they got colonised.
Europe has surpassed others after the desasters of the plague, episodically, in the 14th century, after losing 2/3 of its populations, there more "rooms" to develop, so to speak, as the taxes were lower afterwards, Feodalism disappeared (no more serfs and slave-like work), while the productivity increased and we see the end of the last Crusades. They re-populated rapidly, with more marging as there was a new technological "revolution" (minor one).
The Europeans kept on improving their countries through trades, diplomacy (french invention hehe), wars (in-wars between them), crazily-expanded Empires and the vestiges of the Greeko-Roman Civilizations (in terms of Urbanism, Justice, Institutions, with the re-discovery of the Ancient Philosophers and the beginning of the "Enlightement Period").
Quite fascinating story, in my opinion, and today we are witnessing the emergence of Asian Superpowers; they are just re-appropriating their former roles!