Hmmm. I think you'd need more trade flowing through Byzantium to really get the population growth and wealth needed. Perhaps more Greek settlement in the Black Sea and Caucasus causes more trade through the Strait? That would let Byzantium grow a trading empire through the Black and Caspian seas while using the wealth that brought them to exert pressure on Greece proper.
The Black Sea by the end of the Archaic Period (basically the deadline) was already widely settled by Greeks, even if some of them were in Persian territory. I'm curious if you can think of some good settlement options that weren't exploited till later?
I think i recall someone bringing up this possibility though i don't remember when.
But basically, it was a reformation of the Delian league that moved power away from Athens to Byzantion.
That sounds familiar. I like those Delian Reformation discussions

(I probably suggested something like that tbh)
What if Athens or one of the other big cities suffers a major disaster, causing a need to flee?
And if by dynastic ties, marriage or other reasons, they head to Byzantium? It could be an earthquake, a volcano or some natural disaster, or it could be an invasion that requires the population to evacuate.
Byzantium is just one destination; alternatives include Asia Minor such as Ephesus, or Sicily. Why would colonists choose Byzantium? Or how might it naturally rise to dominance?
IIRC the Romans built the aqueduct of Valens to carry water 50 miles to the city. This was important for its growth. Could such a project be feasible centuries earlier?
The Persians probably had the technology. What if they somehow built the necessary infrastructure? And then the city becomes independent and starts its own little empire?
"What is your PoD?"
"Zeus wrecks Greece"
"Awesome"
That certainly is a possibility, especially if it was widespread and effected many cities. I think Byzantium was a colony of Megara, so perhaps we could have a disaster, or an exile scenario. Either the Peloponessian Wars could see another round, leading to a sacking/burning of Megara leads to their exile, where Byzantion (got to use the right name in Greek, gah, bad RTE, bad!) effectively offers them shelter due to their ties. The relatively large influx of population that would lead to would strengthen them in the long run, and they were already capable of conquering their neighbours (see Chalcedon) historically.
Regarding the idea of an Aqueduct - I'm not sure the population, even with an influx, at this time would require it. My understanding was that the population before Valens was many times larger by the time it was started by Hadrian.
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I'm finding myself quite enamoured by a potential for a Post-Delian League scenario. With Sparta on the rise, anyone who didn't want to live a life under Sparta could be invited to join the Greeks Beyond the Hellespont, a potential faction that could form from the ruins of the league, centred around a potential Byzantion-Odrysian Alliance built on the idea that both whoever rules the Odrysians could make use of the Greeks as allies, and vice versa, effectively enabling the Greeks to play Kingmaker, and provide security. The Greeks likely joining this Byzantine League (to give it a name) out of a mix of diplomatic overtures, and unspoken pressure by the Thracians.
So if we agree that is reasonably peaceful and secure, we could go with disasters or action during the Corinthian War to attract more Greek settlers, farmers, to the Byzantine League, strengthening it and creating effectively a second, more mixed, Greek League of coastal colonies organised in a similar way to the Second Athenian League (just smaller, and outside central Greece).
The advantage this gives us is potentially a stronger Odrysians backed by Greeks that could have the naval logistics of the Greeks to support a major campaign into Macedonia, perhaps being the group that adopts mixed arms and the Sarissa that IOTL Philip used. Its in a region exposed to Scythian horsement (potentially an example for great cavalry warfare, and a source of mercenaries and trainers), Thracian Peltast (a large part of Alexanders Army, and a strong force in their own right) and Greek Hoplites.
Whilst it isn't hegemony, that at least gives us a strong, Byzantion-led League of Greek Cities, with Thracian allies, with Mixed Tactics warfare, with the potential to take the Chalkidike as a result of the suggest campaign by the Thracians - effectively creating a joint Thracian-Greek Hegemony that could flip into a Greco-Thracian one if the Odrysians fall apart like IOTL, opening vast territories to Greek colonisation. (Perhaps a method to weaken the Chalkidikie if they're too uppity, and move their strength.
Essentially, if this butterflies Philip (it changes the succession in Macedonia even if Bardylis exists to invade!) then you effectively see a Greek World split into the Theban/Spartan/Athenian South, Illyrian/Macedonian NW, and Greco-Thracian NE, the latter having both a mineral and agricultural advantage in terms of territory and population because of the divided Thracian majority they can integrate.