This may go into WMG territory, but it's very possible that Nancy actually did think she had her period before she actually did.
The book is set in 1970 and while there were a few short films out about periods, none of them shown really shown visible blood; even Margaret said (in the book) that the film about periods that the class watched didn't show a girl getting her period. It's very possible that Nancy's family didn't talk about periods before and she could have possibly had discharge rather than a true period—and not knowing that periods are actually blood, probably thought she really was getting her period. This explain why she panicked in the bathroom in New York when she actually got her period, getting scared and thinking that she's sick. This can be Truth in Television as girls who were not taught about periods could have similar experiences. The irony here is that while Nancy claims to be the most knowledgeable about sexual stuff and puberty in their friend group, she had no idea how a period worked until it actually happened.
It's also plausible Nancy was just spotting at first; seeing tiny amounts of blood before her actual period started, and thinking it was the real deal. It's not unheard of for people to have a tiny amount of blood the first couple times, and to take a few months to get on a regular schedule and start bleeding the regular amount. Ergo, Nancy might've gotten a little speckle of blood, thought her period was starting, then went months with either very little bleeding each month or maybe even no bleeding at all, and then was caught completely off-guard by her first real period, which would have much more blood than she was used to.
In the film, early bloomer Laura Danker (played by older Isol Young) looks and sounds like she could be Puerto Rican. Puerto Rico has the absolute lowest median puberty age on the planet, making a likely explanation for Laura hitting puberty earlier than her white classmates.
Laura, when ranting about how hard it is to develop breasts before your peers do, brings up that people frequently spread rumors about her being a slut and messing around with teenage boys, and that male teachers stare at her. Reading the book as a tween you feel bad for her, but when you re-read it as an adult, you feel bad for her and realize, oh my God, this girl is twelve and adult men are looking at her sexually.
Even worse, adult male teachers. Just think about that for a second.
Also, young girls who haven't gotten their periods (and who only know the most basic information about periods, puberty, and sex) are calling Laura a slut when they probably have no real concept of what that implies outside of her letting boys "do things" behind the A&P. It makes you wonder what the girls think it is.note It's worth noting that at one point Laura confronts Margaret about what exactly she thinks Laura is doing, and Margaret doesn't actually know..
More importantly, who taught them that it was the worst thing someone could be? Likely their own parents and older relatives. As the book was set in 1970, the second wave of feminism was just starting and the awareness of Slut-Shaming wasn't really present; society was clinging even more (despite the Sexual Revolution) to the Madonna-Whore Complex, and thus it's likely girls learned it from older relatives and adult figures. You have to be carefully taught...
There's another layer to Laura's problems as well, even if she doesn't say it. Having rumors spread about her is bad enough on its own, but Laura is Catholic and fairly devout, and the community she lives in is a relatively small one, so it's likely that there's crossover between her school peers and people in her church. If those rumors gain traction with her church community, it could cause her to be shunned by the church community as well.
