Well as I said it's like Marvel and One Piece mixed. They're born with powers but they only develop during adolescence with few exceptions. Powers vary but usually you can use your powers in a variety of ways, that's where One Piece relation comes in. For example the Lancer of the story has Biological Manipulation as his power. He can change his appearance, accelerate healing by touch or sever muscles and give illnesses. And he can temporarily super charge a persons muscles giving them enhanced strength.
But what I'm more concerned with is how would they fit in in that period?
I suppose that's true, but what about monotheistic cultures or pantheistic cultures like the Native Americans? Would Jewish superhumans be stoned or cast out as demons? Would Native American superhumans be seen as evil spirits or as ones blessed by spirits?
We also have to think of the technology cause the story takes place about 700 years later, Ancient Greece is just where they're introduced. I mean would superhuman powers advance technology at all? Would they already be in musket and hand cannon tech by that time
I should think superhuman powers do the complete opposite. Much like ancient Greece threw away all it's machinery and automation technology because they thought it useless when they had so many slaves. In this case, if you have super strength, why bother with a lever? Just ask Strongacles to lift the boulder for you.
But not everyone is going to have super strength, and in a city maybe one or two people alone would have it. There would be no way to predict who gets a power and what power they get so in the end it would be less productive.
But I'm saying if one or two people gain a high intelligence would they not perhaps eventually make agricultural, scientific, etc etc... advancements earlier?
I wouldn't count out Jean, especially as she taps into the Phoenix Force.
Honestly though if these powers are only confined to a few people the net effect is probably going to be one of two things.
1)Particularly spectacular individuals would probably gravitate towards positions of power and may eventually form a type of hereditary aristocracy on the basis if Might Makes Right and explaining their powers by divine ancestry.
2) Give later periods a lot more legends to riff off.
If you really want to change things drastically you need the equivalent of [[X Men Forge]] or some other power set that turns them into a Gadgeteer Genius that can then kick start an industrial revolution.
Hmmm... plot bunny being born. A group of Badass Normals teaming up with a bunch of... for lack of a better catch all term Sparks who have powers that are considered second class compared to you're average Flying Brick and others with more obvious power sets.

I'm planning a book about a world filled with superpowered individuals, kind of like Marvel mixed with One Piece in a way. I'll get to more on that later but here's the main thing.
How would superpowered individuals change the world if they were introduced during the time of the first Persian War?