It depends on the species and world building.
Elves usually age slowly, to the point they aren't considered adult until they turn 100 or so.
Some continue to age even after they become adults, turning into old bags of wrinkly flesh like Yoda. Dragons usually fall into this category too, oddly.
Some stop aging the moment they become immortal like Vampires.
And yeah, things like Fairies are usually never children to begin with.
So, you need to understand the reason your creature is immortal and pick a method that suits it. You may also want to consider the culture and such of your creatures before deciding.
Elves have a mostly human culture, but they isolate and adore their children so they have time to grow up.
Creatures born as adults don't understand what it means to be children, for better or for worse.
Vampires might be willing to foster a human for decades before finally turning them.
Did you have a specific goal in asking this?