Goslings start to get in their feathers by week two in their tail. They look completely like miniature geese by 12 weeks of age. 
With Pilgrims they should be friendly and sociable _even during_ breeding season. Good Pilgrims are bred to be laid back and friendly - that's one of the traits the breed is required to have. During breeding season they may start hissing, but you will never have to worry about being attacked. 
Geese in general are much more laid back than your other birds. They're a lot like turkeys, and the explanation I was given for why makes a lot of sense. 
Geese are extremely large birds. Their defense isn't to run and hide like your smaller birds, so they don't bolt at the first sign of danger. Because of this, they're less likely to be intimidated by something - especially if they're in a group. When they feel threatened, they'll keep their distance, but then they'll turn around and look at the potential threat and chat about it to one another. 
Your goslings - especially Pilgrims, American Buffs, Sebastopols, and Dewlap Toulouse - will always be happy to see you. Louder geese will blast out to let everyone else know their favorite person is in the yard and come waddling over. 
They're big puppy dogs. A lot of them grow out of the habit of wanting to be held or picked up (if they ever wanted to be picked up in the first place), while others will try to crawl into your lap. I have one Pilgrim gander that wants to be held so he can look around and will constantly try to crawl into your lap looking for treats (we taught him that if he sat patiently in our lap while we live harvested down he got snacks...he took it a step farther and decided lap = treats 
. 
These guys are absolutely incredible. More people need to be bitten by the goose bug (instead of the goose 
 and help promote raising and keeping friendly, rare geese for the homestead.