“This has got to stop, and the only way they hear, the only way they hear us is through violence, through the means that they use,” she said.

She suggested that the destruction of police property was appropriate.

“People are angry because the police are never held accountable,” she said.

In the video, she was standing near a convenience store, according to people with knowledge of the investigation, where some of the materials for the attack were purchased.

Mr. Mattis’s lawyer, Sabrina P. Shroff, said at an earlier hearing, “The government tries to argue to this court that Mr. Mattis’s behavior — assuming that they can prove it beyond a reasonable doubt and conceding nothing at this point — is indicative of who Mr. Mattis is. They are clearly wrong.”

Since the arrest of the two, friends and family members are struggling to understand what happened.

Ikenna Iheoma, the friend who spoke with Mr. Mattis the day before the protest, said they had never discussed violence against the police. “We went to private high school,” he said. “That’s not the lane we go to. We try to intellectualize and come up with policy solutions.”

Several friends said Mr. Mattis had not told them that he had lost his job. He did, however, tell one friend in April that he was already interviewing at other firms.

Mr. Mattis, a reliable presence at Princeton’s boisterous annual reunions, had been planning to attend a virtual event for his 10-year reunion on the day he was arrested, friends said.

Salmah Rizvi, who was also at the May 29 Zoom talk with Ms. Rahman, said nothing seemed unusual about Ms. Rahman’s recent behavior.

“She was in a good spiritual state this past month,” said Ms. Rizvi, who called Ms. Rahman her best friend. “She’s always been vocal about the important role of nonviolent resistance in seeking change.”

Ms. Rahman was a staff lawyer at Bronx Legal Services, helping poor tenants facing evictions. Her supervisor, Jackeline Solivan, said she was deeply committed to the job and, like other colleagues, had been stressed about pressures on her clients caused by the outbreak.

Friends said they were not aware that the two were going to attend the protest that Friday, the second night of demonstrations in New York City.

In the middle of the chaos, shortly after midnight, Mr. Mattis and Ms. Rahman, while riding around in his minivan, pulled over near the 88th police precinct at Classon and DeKalb avenues.

Ms. Rahman stepped out of the passenger seat and threw a Molotov cocktail through the broken window of an empty police car, setting the dashboard on fire, according to prosecutors, who said the episode was captured on surveillance video. No one was injured.

Andrea Wangsanata, a high school classmate, recalled that Ms. Rahman was often “vocal and adamant, advocating on the side of people who were systematically oppressed.”

Ms. Rahman was born in Pakistan and grew up in Bay Ridge, Brooklyn, a neighborhood with a large population of Muslim immigrants. The neighborhood came under intense police scrutiny after the Sept. 11 terror attack, which became a defining experience for Ms. Rahman, childhood friends said.

Through college and law school at Fordham, she lived primarily at home with her mother. Her father died in 2012.

While Ms. Rahman pursued public interest law, Mr. Mattis took a more lucrative path.

Martin Guggenheim, one of Mr. Mattis’s law professors at N.Y.U., remembered him explaining — “sometimes apologetically” — that he wanted to work at a law firm because he was the first person in his family with the opportunity to have that kind of career.

Mr. Mattis grew up in East New York at a time when the neighborhood was among the poorest and most violent in the city. Throughout his childhood, his mother, a Jamaican immigrant who worked as a home health aide and youth counselor at a group home, fostered several children.

He struggled with literacy in the early years of elementary school. By middle school, he became a voracious reader, a neighbor said.

He was a football player in high school and briefly played rugby at Princeton, where he was also president of the Black Student Union and a member of Cap and Gown, one of the university’s exclusive eating clubs.

His college friends said they were particularly stunned by the allegations because he was known as a peacemaker on campus, the one who brought students of color to parties hosted by wealthy white students.

In recent years, Mr. Mattis shared posts on Facebook drawing attention to protests against police brutality and the death of Eric Garner in police custody.

Last summer, Mr. Mattis’s mother died of cancer. He moved back to her house in East New York and became responsible for the three children she was fostering, which his half sister said had been their mother’s dying wish. The children are all under the age of 11.