Until the Portuguese began the Age of Exploration, the world always had several cultural centers that developed largely uninfluenced by, and even in ignorance of, each other. The Western Hemisphere might as well have been on another planet from the Eastern. Africa south of Ethiopia was almost as isolated. Australia, too. China was only vaguely aware of and not even vaguely interested in India, let alone lands further west. And then all that changed rather abruptly, on the historical time-scale.
Imagine that in the Sixth Century B.C., the Greeks win the Battle of Alalia (Corsica) against the Etruscans and Carthaginians, strengthening their colonizing position in the western Mediterranean – to the point where Greeks are able to get more or less safely through the Pillars of Herakles, and then they can sail up and down the coasts and colonize. Soon Greek colony towns dot the Atlantic coasts of Africa and Spain and Gaul – all in continuous competition with the Carthaginians, breaking out in war periodically – which spurs technological progress. Eventually one nation or the other – doesn’t matter which, the other soon copies it – hits on the essentials of deep-sea sailing technology, and the Age of Exploration is off and running. (And if Rome rises in this timeline, then the Romans will get deep-sea sailing technology too.)
But, it goes rather differently than in the 15th Century in our timeline: Neither the Greeks nor the Carthaginians are numerous enough or technologically advanced enough to conquer the native empires everywhere they go. What each does, instead, is found a global network of politically independent (at least, the Greek ones are, that’s the Greek custom) coastal colony towns, each farming the immediate neighborhood, and trading (for slaves among other things, no doubt) with the “inland barbarians,” and trading with the rest of the world. The Old World diseases spread to the New World before they get the chance to grow quite so virulent as they did in OTL – probably a lot more Indians survive contact. The introduction of Old World crops and animals to the New World and vice-versa happens in antiquity, so gradually perhaps that nobody is really sure where the potato came from. China is no more isolated than any place else, it is regularly exposed to the wider world – and to the fact/idea that other, powerful civilizations exist – from the Warring States period on.
And, any idea – whether technological or scientific or philosophical or religious or political or artistic – that once becomes current in one of the world’s centers of civilization, will soon be known or known of in all the others. Greek philosophers are thoroughly exposed to the philosophies and religions of India and China. Everybody the world over hears about this Greek thing called democracy. If anyone invents the printing press or the stirrup or the rigid horse collar, the whole world has it before long. Greek musicians will be exposed to Indian and Chinese music.
And the “inland barbarians” – in the Americas, in Africa, everywhere – might not be such pushovers, because they get exposed to everything their Greek or Punic neighbors on the coasts have and, not being in immediate or constant danger of being conquered by them, have the space and leisure to copy it.
How does history, generally, go in this timeline?