As [the answer to a related question][answer] indicates, the Hogwarts Acceptance Letter is **not** delivered on the students' birthday, but at the start of the summer before the students start at Hogwarts.

Note that Harry's letters started coming in _before_ his eleventh birthday. Only because of Vernon Dursley's refusal to let Harry read his mail did it become necessary to deliver the letter in person on his birthday.

This means that if muggle-born students need an escort to Diagon Alley, one will be provided for them _then_, not on their birthday, but when they go shopping for school supplies.

[answer]: https://scifi.stackexchange.com/a/21935/19561