I say the last few weeks but really it's a constant source of worry for kids in big families.
Personally, I never had a problem, magical from the start. Hermione and Harry didn't know they were were magical until they read their letters.
My kids are typical, magical born kids. Their only worry is being a Squib. (something neither are from the fact that I can still see the mess on my kitchen floor where the plates have shattered.) They have had experience of family members going to various schools and now that Sevie is going to Hogwarts the only question that seems to have been plaguing her has been what house she will be put into.

SEVERINA WEASLEY: Mum? What do you think I will be sorted as?
MUM: I really don't know sweetheart there are 4 houses and you could suit any of them.
SEVERINA WEASLEY: Dad? What do you think?
DAD: The right one for you.
SEVERINA WEASLEY: But I am a related to Slytherin aren't I?
MUM: Yes but that doesn't mean we are put in that house.
BERTIE WEASLEY: yeah look at Mum
SEVERINA WEASLEY: Ok so Badger, Eagle, Lion, Snake... I like all those animals.
DAD: You forget the most important. Kindess, Intelligence, Bravery and Cunning.
SEVERINA WEASLEY: What about friendship?
MUM: Yes that too.
SEVERINA WEASLEY: But what if it puts me in the wrong house.
DAD: I'm sure it won't, no mistakes.
SEVERINA WEASLEY: You said it did Uncle Severus WRONG.
MUM: Ah well he was probably just very complicated.
SEVERINA WEASLEY: can't I be complicated? can't I be all those things?
DAD: Yes you can.
MUM: But the point is to help you find the house that will push you towards what you need to be because it is within you somewhere and the sorting hat can see that.
SEVERINA WEASLEY: So just because I'm put in Hufflepuff
DAD: Doesn't mean you're not kind.
SEVERINA WEASLEY: And if I'm not in Slytherin?
BERTIE WEASLEY: Means you can't win people over.
MUM: BERTIE! Whatever you are in you will be fine.