Why did English become a universal language and when?
Solution 1:
English became the lingua franca around WWII, but it was already used all through the British Colonial Empire, establishing it in North America and Australia among others. here is a citation of Wikipedia:
It[English] has replaced French as the lingua franca of diplomacy since World War II. The rise of English in diplomacy began in 1919, in the aftermath of World War I, when the Treaty of Versailles was written in English as well as in French, the dominant language used in diplomacy until that time. The widespread use of English was further advanced by the prominent international role played by English-speaking nations (the United States and the Commonwealth of Nations) in the aftermath of World War II, particularly in the establishment and organization of the United Nations.
[...]
When the United Kingdom became a colonial power, English served as the lingua franca of the colonies of the British Empire. In the post-colonial period, some of the newly created nations which had multiple indigenous languages opted to continue using English as the lingua franca to avoid the political difficulties inherent in promoting any one indigenous language above the others. The British Empire established the use of English in regions around the world such as North America, India, Africa, Australia and New Zealand, so that by the late 19th century its reach was truly global, and in the latter half of the 20th century, widespread international use of English was much reinforced by the global economic, financial, scientific, military, and cultural pre-eminence of the English-speaking countries and especially the U.S. Today, more than half of all scientific journals are published in English, while in France, almost one third of all natural science research appears in English, lending some support to English being the lingua franca of science and technology. English is also the lingua franca of international Air Traffic Control communications.
Solution 2:
This is a difficult question to answer because so many of the terms are vague. Even the term "English" is mutable, as there are many dialects and variants used regionally which are quite distinct from one another, with their own grammatical quirks and entirely unique vocabularies.
However, I would say that it was England's massive colonial expansion and the post-colonial retention of English for trade and negotiation that are mostly responsible for it's prevalence - in turn caused by England's naval superiority for many centuries. The aggressively prolific production of English-language media in the early- to mid-twentieth century (Hollywood et al) resulted in prolonged global exposure, and a significant proportion of research and diplomacy was already taking place in English. Nobody can say exactly when its usage gained "critical mass," but I would agree that it was somewhere in the early 20th century.
There are many other universal-communication languages in use (a notable drive in S E Asia to promote "Mandarin" Chinese as a lingua franca is underway) but as you say, none of them so prevalent as English.