Hi there!
Before i address your question, perhaps i would like to point out that some historians draw a distinction between global history and world history.
It can be confusing since the words can be seen as synonymous but there are subtle differences that some historians can argue for and against. Global history is not so much a field of history as it is a perspective or lens in which we can study history. On the other hand, world history is a study on the long time frame of the world. This is where historians study the history of civilisations.
If i may quote Prof. Haneda Masashi in an AAWH Conference given in May 2015: the "world historian looks at the world as the ultimate unit of analysis from the appearance of Homo Sapiens...to today for the sake of creating an integrated narrative of human societies" while the global historian "looks at a world that increasingly tightens as a historically emerging functional unity in the search for worldwide connections that transform the shape of societies locally as well as enhance the articulation of a globalized world"
As such, you can see that there are differences in the two forms of history, while the semantics might lead you to think otherwise.
Going back to your question, global history could be seen to develop around the 1990s where historians like to think of the "spatial turn". This is where traditional notions of space is questioned; and hereby exists flexible notions of distance, scale and boundaries - a "trans" world so to speak where you hear of buzzwords like "transnationalism". You could attribute it to the end of the Cold War where the role of transnational forces and regional associations become increasingly pronounced in the writing of history. One such example would be Ian Tyrell's American Exceptionalism in an Age of International History
Going by the definition of World History therefore, it can be pointed to an earlier period where historians such as Toynbee and Spengler begins.
Authors like the late Christopher Bayly (The Birth of the Modern World, 1780-1914) would be a good example of this sort of global history.