Hmm. What would the immediate ramifications of Cyrus II of Persia being absent from the documents of history, perhaps killed at the Battle of the Persian Border in 551 BC? According to
this map, this would leave Astyages' Media battered and bruised yet intact and victorious over the Persians, who would command his armies to raze Pasargardae to the ground, subjugating the Persians under iron fisted brutality that would make Scythians blush. Perhaps Media could fragment from revolts by less able men than Cyrus...
Meanwhile, Babylon would remain an independent state able to repel the Medes if need be (for the remainder of the century at least), and may or may not keep Nabonidus on the throne, depending upon his leadership and sanity. Somehow I doubt that, given that the Priests of Marduk would be more than happy to depose and execute him, elevating one of their own as regent for the abler Belshazzar to be controlled by (at least during his childhood.) I would like to see further scientific and technological feats performed by Babylon scientists and astronomers occur in the mean time.
In Anatolia, Lydia would also remain independent. Under Croesus' continued hand Lydian wealth and culture would continue to develop and flourish, perhaps rivaling that of Greece's. If the Medians fragment or are at least distracted by revolts and wars, Lydia potentially could unite Anatolia like the Hittites before them...
In Egypt, the 26th Dynasty of Egypt would continue unconquered under Amasis II and his kin. Having just conquered Cyprus and improved relations with the Greeks, Amasis' policies would continue to bring Egypt into new levels of wealth and prosperity not seen since Rameses' time (?). I wonder if he would claim the Throne of Cyrene in the future, or push back the Kushites...
And then there are the Greeks. Boy would their history be significantly altered if the Persian Empire never existed. Where to begin? No Ionian Revolt? No Greco-Persian Wars? Would Democracy be smothered in it's cradle in Athens? Could Sparta dominate in it's place? So many bloody questions...
And I wonder if the PoD could reach Italy, and prevent the founding of The Roman Republic? The butterflies from that point on for the entire history of the World would only increase exponentially from there. But what if we're creative enough to build that world further than 500 BC? Is anyone feeling lucky enough to put on such a great task?
Can this be green-lit for production?