Nearly everyone in this thread is completely missing the actual request of the OP, which was
not to figure out how you could end the century with a united world government with a PoD in 1900, but instead to create an
ideological movement in favor of world government and tearing down the barriers between nations, etc., with a certain degree of influence, enough that maybe a few governments officially support it and it's not a fringe movement but reasonably popular. It does
not have to actually succeed, merely attain this degree of influence at some point whether or not it declines thereafter.
But, as it so happens,
this is historical! After the end of World War II, there was for a period of time a fairly active movement that could be described as "pan-Humanist," dedicated to supporting the United Nations and generally some kind of global governance. This was expressed in organizations such as
UNA-USA or the
World Federalist Movement, which at their peaks in the late 1940s attracted tens of thousands of members and which had links, albeit indirect, to actual national governments. However, by about the mid-1950s they began to decline, and by the 1980s or so were essentially fringe groups, especially in the United States where conspiracy theories and kvetching about the United Nations became particularly strong and support for any kind of global government was thus heavily disfavored.
So it would actually be totally reasonable to say that this WI is what actually happened, and therefore no changes need to be made. However, assuming that the OP had in mind something more long-lasting and influential than this brief mid-century period when forming some kind of global government was a serious and somewhat popular political opinion--which the comparison to pan-Africanism certainly suggests--still doesn't suggest that we need to abolish states, or any state, to achieve it, just extend this period and give it deeper roots in public opinion so that there's still a committed and somewhat noisy minority in favor today. This isn't
easy, mind you, since a lot of their success had to do with that brief period when the United States alone had nuclear weapons and many people thought that some kind of international control would be the best way to avoid nuclear war, but it's sure a lot easier than working out how to turn the United Nations into a global government.