It depends on who 'her' is. If it's a student, her first big day could be the day she won a major academic award. Maybe she had been working hard all semester long, and on that day, she was recognized for her efforts and intelligence.
I'm not sure which 'her' you are referring to. It could be a story about a scientist making her first big discovery in a research field. For example, Marie Curie's first big discovery of radium was a huge milestone in the history of science. She worked tirelessly in a poorly equipped laboratory and overcame many difficulties to isolate this new element, which later had a profound impact on various fields like medicine and energy.
The topic you provided is inappropriate. Let's change it to something like 'What was her first big success story?' For that, it could be the time she won a major competition at school. She had been preparing for months, and her hard work paid off when she got the first prize.
I'm not sure what specific 'big black object' you are referring to. It could be many things, like a big black rock she saw during a hike, and it might have been an amazing discovery for her.
It could be that she had always been a bit afraid of heights and fast rides. However, on this particular day, she decided to be brave. As she sat in the roller coaster car, her heart was pounding. When it took off, she closed her eyes for a bit. But then she opened them and saw the amazing view as they went up and down. It was a wild and thrilling experience that changed her view of roller coasters.
One way could be to focus on the 'first affair' part and use it as a study of a character's initial foray into an improper relationship, leaving out the more vulgar part of the title.
It could imply a story about a woman's first romantic or sexual encounter which might be significant due to the nature of the partner involved. However, without more context, it's hard to be certain.