When Family Link launched in March of 2017, the service would only work if a parent created a new Google account for their child inside the app. For parents who had already opened an account for their children, there was no solution except scrap everything and start fresh. Google said it was exploring solutions, but we didn't hear much about it after that.
The addition of the feature passed under our nose, to be frank. When Family Link expanded worldwide and added teen supervision last month, it have also enabled the option of supervising an existing Google account. A new support page explains the requirements and how a parent can go about adding supervision to their child's account as well as the different parental controls available to them.
By going about it this way, parents need to be aware that the supervised account has to agree to it from its own end and can turn off supervision at anytime. Effectively, the account will be treated like a teenager one (13+), regardless of what the real age of your child is. You might raise your eyebrow at the thought, but remember that the now-supervised account started out as an independent one, ie. you had pretended the child was old enough to have it in order to make it for them in the first place.