Everybody knows that your Hogwarts letter should arrive on your eleventh birthday. But careful reading suggests that no, it doesn’t. Harry’s only did by coincidence. The first letter actually arrived on July 24. It was only because of Uncle Vernon’s comical attempts to avoid the letters that Hagrid had to deliver it in person a full week later, and it was only by coincidence that it was Harry’s birthday when it happened. So no, it doesn’t have to come on your eleventh birthday.
Except Rowling doesn’t seem to have this quite fixed in her mind. After all, here’s what she wrote on Pottermore about McGonagall:
“Minerva never forgot how much her mother cried, when the letter of admittance into Hogwarts School of Witchcraft and Wizardry arrived on Minerva’s eleventh birthday …”
Minerva McGongall’s birthday is October 4. If she did receive her letter on her eleventh birthday, she then had to wait almost an entire year to actually go to Hogwarts.
Furthermore, Rowling writes this on Pottermore about Harry’s letters:
“Even though Petunia was raised alongside a witch, she is remarkably ignorant about magic. She and Vernon share a confused idea that they will somehow be able to squash the magic out of Harry, and in an attempt to throw off the letters that arrive from Hogwarts on Harrys eleventh birthday, she and Vernon fall back on the old superstition that witches cannot cross water.”
Well, if Rowling thinks that the letter arrives on a person’s eleventh birthday, I guess they do. Like so many little inconsistencies in the first book, Harry’s early-arriving letters must be a fluke, kind of like the Quidditch match which was inexplicably held, not at 11 am like every other school match, but in the late afternoon in chapter 13 of Philosopher’s Stone.
Or maybe whoever brought the letters was so eager to see Harry after all those years that he or she delivered the first letter a bit early. There’s nothing to indicate that the letters were sent by owl post, after all, despite what we see in the film. In fact, it’s highly unlikely that they were. Owls wouldn’t know that Harry moved to a new bedroom, and they certainly wouldn’t be able to magically insert letters into a dozen eggs. Someone was clearly watching from nearby, orchestrating the whole letter event, someone with more than a little magical skill and a clever imagination. McGonagall herself, perhaps? Once again, hanging about in Privet Drive disguised as a cat?