When the authors emphasize that, when a child gets a pair of gender binary glasses, it's just their first pair, they mean to say that?

This is because the "Young children perceive gender in their society but differently than they may when they are adults". Between 3-5 years children have a vague notion about the genres, sometimes they believe that these can be changed to choice, or that despite being of one gender can do things of the other gender, like a child wanting to be pregnant. As they grow they not only understand the biological differences, they also understand the social differences of the genres and begin to identify more with one in particular.