No. 🙂 If it did, there'd be no market for training bras, and most cis girls/women would have had issues. (*Binding* can harm breast development, but that is far more compressive than any marginally fitting bra should be - and at the initial stages of growth, I would think the pain of compression would let you know if you were wearing a bra that fit THAT poorly.)
Breasts can take 3-5 years or longer to finish development, too; personally, I didn't hit the end of the growth phase until about 10 years later.