If we're talking about when a unified world would have been technologically feasible, I guess one way of determining that would be to look at ancient empires like Rome and China, figure out the response time of such states (how long it would take a ruler to get word from his minions and back again, how long it would take to respond effectively to rebellion or incursion), and then calculate when technology placed the entire earth in this potential response time frame.
My guess would be technologically the earliest time you could get a unified world would be sometime in the 1800s (or equivalent level of technology). Put together all European colonies and conquests and imagine it all being done by one state, you'd have something close to a world empire.
Politics, of course, is a different matter, as OTL nicely demonstrates (in many ways the present world is far smaller than the Roman Empire in terms of effective distance; you can travel from one end to the other in a day or two, and get a message from one end to the other in an instant).
I think it might just be an accident of history that this didn't happen. Have the industrial revolution happen in a more politically unified civilization like China instead of a politically fragmented one like Europe and I could see the world ending up like this. So a pre-1900 POD might be a good bet for this.
As for the earliest possible date this could happen ... maybe if you could somehow get a scientific/industrial revolution going in ancient Egypt or Sumeria or Shang Dynasty China...
You are definitely on to something. Look at the time for communications and travel (and the amount of communications and travel) in ancient empires and extrapolate it to the whole world, and you do get something like 1800s tech, even conceivably early 1800s tech, but probably more the telegraph and steamship era.
But I don't think that's the whole question. We've already identified the *time* it takes for communications and travel/trade and the *amount* of communications and travel/trade. I think you also need to look at the *duration* of the communications and travel/trade area. In other words, we didn't see the Roman empire come into being as soon as the mediterranean became a functional unit. Instead, it was only when the Med had been a communications and travel/trade area for long enough to have a more or less common culture base (hellenism) that you saw a region-spanning empire form. So you're probably looking at a delay of a few centuries after you reach 1800s tech levels before a world empire becomes very feasible.
I would also suggest that you probable need the military technology to be conducive to professionalization and specialization, which suggests that the mass musket and rifle armies of the 1800s probably aren't ideal for world-empire formation, but I'm less sure about that.
I think the ideal scenario for earliest possible globe-spanning empire is as follows:
have an extremely early agricultural revolution in an area that will be fairly isolated from most of the world until its fairly advanced. In other words, the idea here is that agriculture and other innovations don't "seep out" to the rest of the world until the area of origination is quite technically and culturally advanced, comparatively speaking. This is kinda tough to do, because at the same time you need an area large enough to actually support a civilization. Say you get a few early geniuses in Australia and you get an agricultural revolution there some 30,000 years ago. Add a few more millennia and then suppose that you have an Australian civilization that has finally developed naval vessels with the sophistication to go on long sailing voyages at distant speeds.
You will then have an explosion. At this point Australia will have more population than the rest of the world put together, all the diseases, and massive economic, military, and cultural superiority. Non-Australians will more or less assimilate if they survive with any significance. Skip ahead a few centuries or a millennium, The end result will be large settler or mestize type nations all sharing a related material culture, religions, and probably even language. Given time, and perhaps some continued technical advance, though that isn't necessary, a loose world empire would be feasible.