According to Rita Skeeter, magic will invariably have manifested by age 7
The timing was significant. Ariana was barely seven years old when she
vanished from sight, and seven is the age by which most experts agree
that magic will have revealed itself, if present.
Harry Potter and the Deathly Hallows - Chapter 11
That being said, Rowling did originally plan to have a character (possibly Petunia Dursley) who manifested magic later than 11. This character arc was shelved which makes the existence of "late bloomers" non-canon since we don't see or hear of any of them in any of her writings.
Q. Will there be, or have there been, any "late blooming" students in the school who come into their magic potential as adults,
rather than as children? By the way, I loved meeting you, and hearing
you speak, when you came to Anderson's in Naperville. I can hardly
wait until you tour again.
JKR: Ahhh! I loved the event at Anderson's. It was one of my favorites. That is completely true. No, is the answer. In my books,
magic almost always shows itself in a person before age 11; however,
there is a character who does manage in desperate circumstances to do
magic quite late in life, but that is veryrare in the world I am
Barnes and Noble interview, March 19, 1999