ALBANY — The Roman Catholic Church, the Boy Scouts, schools and hospitals, and the late financier Jeffrey Epstein are some of the targets named in a flurry of sex abuse lawsuits filed Wednesday in New York as the state began accepting cases once blocked by the statute of limitations.

Hundreds, if not thousands, of lawsuits were filed as plaintiffs rushed to take advantage of the one-year litigation window, created by state lawmakers this year to give people who say they were victims a second chance to sue over abuse that, in many cases, happened decades ago.

Those suing Wednesday include a woman who says she was raped by Epstein as a teenager in 2002. She filed against Epstein’s estate and three of his associates. Similar lawsuits from other women who say they were abused by Epstein are expected.

Other suits filed Wednesday include one from 45 former Rockefeller University Hospital patients who say a renowned endocrinologist molested hundreds of boys over more than three decades.

Hundreds of others sued the Catholic Church or one of its several New York dioceses. Among them is Peter Vajda, who said a religious brother molested him when he attended a Catholic boarding school in the Bronx in the early 1950s.

“Now it’s their turn. Now it’s their time,” said Vajda, now 75 and a Georgia resident. “And I want them to get everything they deserve in the way of punishment.”

Another suit filed Wednesday accused former Albany Bishop Howard Hubbard, who retired in 2014, of sexually abusing a 16-year-old boy in the 1990s.

An attorney for Hubbard, 80, denied the claim.

“I can tell you without any hesitancy that the allegation is categorically false,” Terrance O’Connor said.

The state’s statute of limitations had been among the nation’s most restrictive before state lawmakers extended it earlier this year for new cases. The Child Victims Act gives victims until age 55 to file lawsuits and until age 28 to seek criminal charges, compared with 23 under the old statute.

That law, which passed following more than a decade of debate in Albany, also created the litigation window.

“This is a momentous time for courageous survivors who have waited so long for justice in New York,” said Jeff Anderson, an attorney whose firm, New York-based Jeff Anderson & Associates, filed molestation lawsuits Wednesday on behalf of hundreds of clients.

Institutions that have long cared for children — such as the Catholic Church and the Boy Scouts, as well as private and public schools and hospitals — are girding for what could be a devastating financial blow. A similar law passed in 2002 in California resulted in Catholic dioceses there paying $1.2 billion in legal settlements.

A compensation fund for sexual abuse victims set up by the New York Archdiocese in 2016 has paid out $65 million to 323 people, the archdiocese says. Those victims have waived their right to file lawsuits. The archdiocese is also suing more than two dozen insurance companies in an effort to compel them to cover abuse claims, anticipating that insurers won’t pay the claims filed during the litigation window.

The leaders of the Catholic diocese covering Long Island have been working “for months with financial and legal experts to prepare for this day,” according to a statement, which added that parish donations aren’t being used to fund victim compensation.

“Our Church continues to suffer as a result of past sins of sexual abuse of minors,” said Bishop John Barres of the Diocese of Rockville Centre. “Victim survivors of abuse and their families also continue to carry the terrible effects of that abuse.”

Brian Toale, one of those who pushed lawmakers to approve the litigation window, said the lawsuits are as much about empowering victims as financial compensation. Toale, 66, said he was molested by an employee at a Catholic high school he attended on Long Island.

Toale’s suit against the Catholic Church was filed early Wednesday.

“Every time a survivor comes forward, there’s another survivor who finds the strength,” Toale said.

Advocates, mental health experts and victims themselves say it often takes years for people molested as children to speak out about their trauma, even to a loved one. Sometimes victims say they didn’t think they’d be believed. Others say the shame, embarrassment and fear were too much to overcome.

“We only get one childhood, one adolescence,” said Jack Traub, a 55-year-old Staten Island attorney who says he was molested by a doctor at Rockefeller University Hospital 45 years ago. He said that as a result of the trauma, he’s had trouble forming and maintaining normal relationships all his life. “I can’t go back. It is what it is.”

Traub is one of 45 plaintiffs in the suit filed against Rockefeller just minutes after the window opened by the Seattle-based firm of Pfau Cochran Vertetis Amala, which also filed cases against the Boy Scouts and the Catholic Church.

The doctor, Reginald Archibald, has been accused of molesting hundreds of child patients over a 30-year period. He died in 2007. Rockefeller contacted former patients, offered free counseling and conducted an internal investigation that found Archibald “engaged in acts of sexual misconduct and sexual abuse toward many of his patients.”

“Rockefeller University is committed to acting responsibly and working constructively with former patients of Dr. Archibald,” the hospital said in a statement. “We profoundly apologize to his patients who experienced pain and suffering as a result of his reprehensible conduct.”