They grow into adulthood at the same rate as humans, but after that point they age at a slower rate.

As per the PHB, page 23:

"AIthough elves reach physical maturity at about the same age as humans, the elven understanding of adulthood goes beyond physical growth to encompass worldly experience. An elf typically claims adulthood and an adult name around the age of 100 and can live to be 750 years old"

And page 20:

"Dwarves mature at the same rate as humans, but they're considered young until they reach the age of 50, On average, they live about 350 years."

So i did get some things mixed up, for Dwarves it's 50, not 100. Same idea though.

I know it sounds weird at first, but It actually makes a ton of sense. I mean, even outside of fantasy, the amount of time an animal takes to reach maturity isn't really proportional to how long it lives, it has more to do with its intelligence, which is about the same for all D&D races. For a lot of animals, reaching full maturity only takes a couple of months tops. Turtles can live way longer than humans yet they mature in about 5 to 8 years depending on the species.

Humans are already pushing it with about 2 decades worth of growing, having to spend a literal century as a kid, especially in a world as dangerous as the forgotten realms would be insane.