So the parents of Percy, Annabeth, Luke, Nico and Thalia are all gathered from different times by the fates. (you can change that and make it someone else if you like, I don't care.)
Sally and Poseidon came from when they were still together and Sally had just gotten pregnant. Frederick and Athena were from a few days after Athena had left Annabeth with her father. May and Hermes had come from two weeks before May had attempted to take the job as the oracle. Maria and Hades from a month before their apartment crumbled. Beryl and Zeus from when Zeus was with Beryl for the second time and Jason had just been born. Rachel's from when she when she was ten and just realizing her abilities.
Pretty much from when their families had still been sort of functional.
They are left with instructions to read the books they have been provided with. The first none other than Percy Jackson and the lightning thief. After everyone has sorted who everyone was and when they had come from out bringing Hades and Maria up to speed on modern grammar, inventions and how WW2 ended Athena began to read the story.