Starting with the death of Alexander would provide a good timeframe. You have the Macedonian empire that is breaking up and all the Diadochi are still at war, and there are no decided borders yet. Rome would be conquering city states in Italy at this point. And in the east you have the rising Mauryan Empire, born out of the grand and huge old Nanda kingdom of Magadha, and it controls the entire northern India, and tensions will soon lead to war with the Seleucid Empire for entire eastern Persia.
That start date can be interesting because firstly, there can be alternative history because Diadochi are still not fixed rulers of a particular area, they are still fighting for existence and control and there are many of them. This can be prevented. Secondly, Mauryans historically defeated the Seleucids and took entire eastern Persia from them, resulting in Seleucids losing all eastern territories but will then have a defensive ally who isn't threatening them, leaving them free to focus on the Ptolemies in the west. This too can be prevented, and may result in alternative history because Mauryans had an extremely capable and organized army and could've expanded westwards in Persia and Mesopotamia easily.
Thirdly, there will still be Samnites (probably), and you can prevent Rome from rising entirely. Or probably kill the Italians as Greeks and reestablish their waning rule there. And finally, you have the chance to play Brennus and take your Gallic warriors on a huge rampaging campaign set to destroy all the Greeks. Historically if Brennus had succeeded, he'd have become an emperor of a huge land stretching from western-central Anatolia to the French coasts and northern part of Iberian peninsula.
And then there was Carthage who could've tried and got involved in the Diadochi wars. The whole scenario is interesting in my opinion, because like Charlemagne date in CK2 things can turn out differently from history.
But I think this could be an expansion material too if not in the base game. Pulling back start dates and implementing new ones is nothing new in PDS games.