Depending on how healthy the puppy is they can go between 5 to 10 days without eating before they become sick and possibly die.
But usually if the puppy is just being a picky eater and doesn't want to eat the food you give them then they'll eventually eat within a couple days to 5 days at most.
The puppy as long as it's not sick will usually eat after they get hungry enough and not allow themselves to starve.
But if the puppy is still not eating after 5 days then you might need to take them to the vet if possible to have them checked out to make sure nothing is wrong.