"Thank you, thank you, for Harry’s birthday present! It was his favourite by far. One year old and already zooming along on a toy broomstick"
-- Lily Potter (DH10)
Toy broomsticks are tiny broomsticks for toddlers, which rise about two feet in the air.
Ron breaks Fred's toy broomstick when he's three (CS8). Two small girls at the Quidditch World Cup were playing with toy broomsticks that barely lifted them high enough for their toes to be clear of the grass (GF7). Harry discovers in Lily's letter to Sirius that Sirius had gifted him one on his first birthday (DH10).
When Sirius gets Harry the Firebolt, he asks him to consider it as thirteen birthdays’ worth of presents. In Lily's letter, however, we see that Sirius has indeed gifted Harry another broomstick on his very first birthday.