That would depend on the size of the village, how isolated, the number of young boys available for apprentices … times of war, the boys could have all been taken away to fight, the smith was left in the village, but the lord still wants his 14 pikes and a sword by the end of the month.
Necessity in a small village, things just need to get done. It could have started by merely fetching/carrying/setting the fire, old enough to be useful, too young to send away.
The key when writing fiction is to make it believable, if the reader/watcher thinks that’s plausible, I can see how it went from A to B to C, then mission accomplished. You may need to spell out more story line for a female character to be plausible/believable, but that doesn’t make it an impossible task.
**edit cause I reached my post as new user limit, so in reply to following thread.
any number of story threads could get around that, easiest being a not smart lord …
But I’d prefer something like … His older apprentice died of the same plague as his wife, and new apprentices are only taken on in the spring, by which time either she’s earnt her place at the forge, or he gets another (who’s not as good as she is - so he doesn’t get rid of her) or as previously said, he doesn’t want to get rid of her, she’s his only child.