Earlier Unity of Ancient Greeks

It's relatively easy: have the Persians win. The Greeks weren't known for their cohesion, but the Persians could make them into a cohesive satrapy, allying with the most powerful Medisers and leaving the enforcement to them. My favourite scenario is Athens - ruled by a proper tyrant - deciding to stick by its allegiance to the great King and helping crush the Spartans in the campaigns of 492-490. Then the Lord Tamishtyklash, Friend of the King of Kings of Iran and Not-Iran, can take his appointed place as satrap of all Akhaia.

Other than that I don't see it. It's not like the Macedonians made it work for very long, either.
 
I think in the period leading up to Alexander, philosphers like Isocrates advocated one of the more powerful city-state leaders "take command" of Greece.

One of the favored candidates was the ruler of Syracuse, while Thebes might have been a favorite as well.

And would the Macedonians have had an easier time of it if they hadn't conquered Persia?
 
The Greek poleis were fiercely independent. You could have unity imposed from the outside, by Macedon or Persia or Rome, certainly. Failing that, it's tough. A sufficient outside threat (like Persia) iOTL brought Greece together TEMPORARILY, but then they fell back squabbling again.

I think the best bet is probably the Delian League. If Athens can be kept from turning it into an Athenian Empire (as they did iOTL), it could be the nucleus for a united Greece. OTOH, I'm not at all sure of any way to keep Athens under control, so that, too, is tough.

If the Delian League can be held together as a federation, probably under successive external threats (Macedon, Epirus, Rome, Persia, what have you), maybe conquering Sparta (who isn't likely to want to join voluntarily)...

Maybe
 
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