I can kind of see what the OPs trying to get at. This is something I can only see affecting recent (African) immiigrants though, so I don't know how much discussion it's going to spur.
I was born and spent most of my childhood in Africa. I lived around black people and rarely, if ever, saw any non-blacks. Because of this, I never really thought of myself as 'black'. I just thought of myself as myself, or my ethnicity (although even that was tough cuz i was an outcast with my own people).
When I moved to North America, it took a while for me to acclimatize to the whole racial dynamic over here.
And to answer you question OP: the first time, I realized I was black, was when people would be 'surprised' because I'd scored the highest in the class or when non-blacks would automatically assume I played basketball or listen to rap just because of my skin color. Also that time I was in the store, and the asian lady kept following me around. That and many other things. it all added up until my identity is right now, literally wrapped around my race. I can't think of myself, as not being black, because me not being black would be me not being me.