I think it was when my child went from cot to bed at about three years of age. It was a low pillow.

I introduced a pillow once they moved into a bed.

Pillows were discouraged when my kids were young. They became used to using one when they would have sleepovers at their nans house, so around age 2-3 years

When they move to a big bed.

I was told to wait until baby indicates they want one, when they start sleeping with hands, blanket or dooner under their head, if they come to your bed and use your pillow, this apparently happens around the age of two, all babies are different though and you know your baby the best, just make sure that their fist pillow is very low profile. 🙂