“Don't do anything I wouldn’t do,” she recalled him saying as she left.

Ms. Helm returned home to California, deeply disturbed by the experience. Embarrassed and scared, she did not call the police, and she did her best to banish the episode from her memory. It was only 17 years later, when she heard Mr. Epstein’s name while listening to a YouTube channel shortly after his arrest in July, that she began to realize who had assaulted her in 2002 .

“I can’t even describe, it was beyond my heart sinking,” said Ms. Helm, now a 39-year-old mother of two living in Oakwood, Ohio . “It was something like a force. I was literally overtaken by horror.”

Ms. Helm is one of five women who sued Mr. Epstein’s estate in Federal District Court in Manhattan last week, accusing him of rape, battery and false imprisonment and seeking unspecified damages.

But the lawsuits have another purpose: to build momentum for changing the statute of limitations in New York and elsewhere for civil claims stemming from sex crimes, which are under growing scrutiny across the United States.

According to Child U.S.A., a nonprofit group that works to expand statutes of limitations, nearly two dozen states have changed their laws related to such rules this year. Many of the changes involved claims arising from allegations of childhood sexual abuse.