Where does it first mention what Hester's sin is?

I think we are given strong clues about her sin when she walks out of prison. The letter "A" on her dress is a big clue followed by,

When the young woman--the mother of this child--stood fully revealed before the crowd, it seemed to be her first impulse to clasp the infant closely to her bosom; not so much by an impulse of motherly affection, as that she might thereby conceal a certain token which was wrought or fastened into her dress. In a moment, however, wisely judging that one token of her shame would but poorly serve to hide another, she took the baby on her arm, and, with a burning blush, and yet a haughty smile, and a glance that would not be abashed, looked around at her townspeople and neighbours.