I did not know this was possible

did you

of course its possible they either get skill from school get an island event or gain skill from their parents

If a child is used to heal another villager they will also gain healing skills. I had one child who was an adept doctor as soon as he turned 14. I suppose in theory he could become a master.

I had a child that gained full Research skill from an event once. It said something about the child not being like other children and it gave the option to have the child research or farm. I chose research and not only was that skill maxed out, but I gained some tech points too, about 1000 if I remember correctly.