Zohran Mamdani has won over many New Yorkers with a hopeful message that he has conveyed at atypical times and places, like at midnight in Queens last week.

In his path from obscurity to front-runner in the race for mayor of New York City, Zohran Mamdani has been propelled by raw political talent, an ambitious, progressive agenda and a diverse base of support.

But as Mr. Mamdani, the Democratic nominee, sprints toward Election Day on Tuesday, many New Yorkers are still struggling with a fundamental question about his candidacy: Is a 34-year-old state assemblyman who, until recently, managed a paid staff of only five, ready to lead the nation’s largest city?

From the congested streets of downtown Flushing to the brownstone blocks of Park Slope and across the five boroughs, interviews with more than 50 New York voters revealed neighborhoods, blocks and sometimes even households passionately divided over the answer.

To Mr. Mamdani’s most enthusiastic supporters, his age and youthful energy are as central to his appeal as the promise of free buses and a rent freeze, particularly at a time when Democrats are demanding generational change in the wake of former President Joseph R. Biden Jr.’s failed re-election bid.

Yet interviews and public opinion polling suggest that a strikingly broad swath of voters — including plenty of Democrats and some of Mr.