As several others have noted, there are some major difficulties. A world that is very multipolar (e.g. OTL in the age of national empires like the British, French etc.) is unlikely to see one of these power utterly win out, because if that's a threat, the others temporarily drop their mutual hostility and gang up on the most threatening one. So that's out. This leaves us a POD related to a more universalist empire, such as Rome, ancient Persia, China, India under the Mauryas, an Islamic Caliphate... And that seems more promising. Suppose one of such great empires goes through an ATL industrial revolution, things could build from there. Bit of a problem, though. There are two things that can happen. Either that industrialisation is on the fast side, or it's on the slow side.
-- If fast, then chances are other powers can't catch up, giving the superpower in question a lot of momentum that just keeps gathering and gathering. It could then conquer the world because it got that critical head start: it was halfway done before any rival could even begin to get its act in order! Of course, such a rapid industrialisation would change society massively, leave the empire unable to properly absorb conquered populations, cause all sorts of cultural and social and economic upheavals (not to mention political ones)... all of which may very well rip the empire apart with the very force of its sudden outward explosion. Imagine all the upheavals the West saw in the period of, say, 1500-1945... but all happening at once within the space of one single century. Enjoy and stay safe, kids! I would rate the chances of an empire going through such vast changes actually surviving the ordeal as very, very slim.
-- If slow, all those upheavals are stretched out over time. Maybe even more stretched out than the aforementioned upheavals were in OTL, allowing for more periods of peace and 'acclimatisation to the new normal'. That way, such a changing empire could process the changes in a sustainable way, and would survive them easily. On the flip-side, that would almost certainly allow rival powers to catch up. Technology wouldn't stay secret forever. In the end, we'd see multiple empires going through the processes of industrialisation, much like various european powers did in roughly the same time-scale. That same thing would happen, but with (say) Rome and Persia or something.
I think only the second avenue offers a realistic path to a 'united world', because the first option almost certainly leads to a chaotic disintegration of the empire. Let's imagine the second, 'slow' course of events. But specifically, let's consider the - not unrealistic - notion that one big empire manages to spark a slow industrialisation, but a major rival catches on (and therefore catches up) relatively quickly. This may well lead to a scenario where multiple rivals flourish (which isn't what we want), but it's not unthinkable that the established power of two existing rival empires allow them to absorb lesser contenders over time. So, to stick with the example, Rome and Persia industrialise, all the while staying fierce rivals. Rome conquers Northern Europe and Africa, while Persia subjugates all of India and Central Asia up to and including Siberia. Rome sails west and captures the Americas, while Persia defeats China while also annexing South-East Asia. In the end, the two rivals each control half the world. At that point, all it takes is for one of them to collapse due to some internal failure, allowing the other to become the sole hegemon, which gobbles up the remnants of its broken rival piecemeal.
Is this an extremely likely scenario? Perhaps not, because the course of events can easily swerve off into some other direction (e.g. multipolar world, or a bipolar one where the two rivals are equally matched forever, or a bipolar one where both collapse in the end). Still, I think that "simply uniting the world" is actually very difficult. A bipolar world is the best set-up, because one simple factor (the collapse of one side) allows for the other to assume absolute dominion over the Earth. So, yeah... that would be my suggestion for having it happen.