With my daughter, getting her first bra was no big deal, and I certainly never tried to make it so. However, as this "sensitive" ad from a 1967 McCalls Magazine shows, getting that all important first bra was a really big deal back then.
To begin with, no one wanted to be the last girl in the group to get her training bra. We all wanted them, at least until we got them. As you can see from this photo, they were typically over-engineered and designed to be one of the most heinously uncomfortable articles of clothing ever invented.
The big feature of training bras that sold all our mothers was that they had these expanding, grow-with-you cups. That translated into two pieces of stretchy lace stuff whose job it was to flatten anything you could develop.
Thankfully we all survived our first training bras, moving on to less engineered and vastly more comfortable models, although I'm not sure we ever really got anything trained.