Alexander, shortly before getting the illness killing him IOTL, decides to manage everything from Athens instead - there were enough competent men in his army.
A few of his officers turn out to be equally gifted, and achieve similar results by applying similar methods - training, observation of the enemy, developing counter measures, integrating the local populace, and so on. The officers usually get the territories they conquer as kingdoms, and help junior officers to become equally successful officers - who wants to live in border territory?
They accept Alexander as their emperor, accept laws made in Athens, and make sure only loyal people succeed them by establishing some kind of school/military career via Athens. It becomes fashion in Greece and surrounding areas to send the kids to military school so that they become King of some country.
If Alexander managed to conquer practically the whole Middle East in 20 years, and only a few of his officers prove to be of only fairly the same quality, conquering Europe, India, North Africa, and so on in another 5 years should be possible - especially as there will be no travelling back and forth by the officers or even the whole army anymore.
The Greek also try to cartograph the world (2nd Pod, sorry), partly for knowing the enemy, partly for finding new land to conquer, partly out of curiosity. They send merchant ships all around the world. Small isles are taken by the colonists and soldiers on board, larger ones are taken later by reinforcements.
Scandinavia, Iceland, east and west Africa, north west Asia, Indochina, and Kasachstan are conquered in the next 5 years.
The plundered goods from the conquests and a part of the tax revenue are used to finance mercenaries for new armies by all the wannabe kings.
By chance, America is discovered meanwhile (3rd PoD, but a probable result of the 2nd PoD). Later, Australia and Antarctica are also discovered.
In Kasachstan, the Greek learn to use horses more efficiently (4th, but not unlikely PoD - despite small horses at the time), thus having new tactics available, and a much higher speed. With a mobile army much earlier than IOTL, China crumbles even more easily than against the later Mongols. Also, most of the rest of Africa can more easily be conquered.
Horses are then also used to overpower the American people. Small colonies there, in Australia, and in other parts of the world claim the whole isles/continents for Alexander. The few blank spots on the map are quickly filled.
A world government is established 20 years after the PoD - 40 years after Alexander began the conquest.
). Namely, that a world government will form when there is a credible external threat, such as an alien power or perhaps just a series of natural disasters like imminent asteroid impacts, and it becomes a priority for the planet to act in concert.