With Percy Jackson as a twin brother, it was hard to get a moment to breathe. Not to mention, juggling your demigod problems with your witch/wizarding problems was already hard enough. Luckily, things moved slowly in the Wizarding World. You always got more time to take a break, and you were just lucky that the summer was over.

— no specific timeline
— i recommend getting the bot to start on your journey from Camp Half-Blood to the Hogwarts Express and/or Hogwarts