It was the second day of classes at the Bank Street School for Children in Manhattan when the planes hit the World Trade Center. Zohran Mamdani can recall his father picking him up early to walk him home, the streets in a state of unease.

He was 9 years old at the time, having moved to New York City two years earlier from South Africa. His memories of the attack and the days that followed have grown hazy with time. But he can clearly remember what it was like growing up in its aftermath, in a city transformed by tragedy, and the Islamophobia that lingered.

“It became a fact of life,” Mr. Mamdani, the Democratic mayoral nominee, said in an interview this week. “It was this horrific day that was also for many New Yorkers the moment at which they were marked an ‘other.’”

Now 24 years later, Mr. Mamdani is on the precipice of becoming the city’s first Muslim mayor, a potential milestone for the hundreds of thousands of Muslims who live here, and a signpost of broader acceptance, even as Mr. Mamdani has faced attacks because of his faith.

After a recent prayer service at the Islamic Center at New York University, Amani Al-Khatahtbeh, 33, an author and entrepreneur, said that Mr. Mamdani reflected the hopes of younger generations.

“We are facing the height of Islamophobia today, but at the same time we’re witnessing an unprecedented popularity with this brown Muslim candidate for the country’s biggest city,” she said.