He has a catchy populist platform. His viral videos exude energy and charisma. Young, left-leaning New Yorkers have joined his campaign in droves.

In a moment when Democrats are hungry for change, those assets have propelled Assemblyman Zohran Mamdani, a democratic socialist from Queens, past more seasoned rivals to emerge as one of two front-runners in the Democratic primary for mayor.

But to actually win on June 24, Mr. Mamdani and his allies confront a fundamental challenge. He must persuade New Yorkers to entrust what many consider to be the hardest job in the country, second only to presidency, to a 33-year-old upstart who until recently managed just five paid staff members.

It is a daunting role for anyone. The mayor of New York City oversees a $112 billion budget, a 300,000-person work force and the bully pulpit of the global capital of finance and culture. The next leader will also have to go toe-to-toe with President Trump as the president threatens to bend the city to his will.

Those who have done the job say there is no perfect training, though most entered Gracie Mansion with more distinguished pedigrees. Rudolph W. Giuliani was a crusading prosecutor. Michael R. Bloomberg was a billionaire businessman. Mayor Eric Adams was a police captain, state senator and borough president.

Mr. Mamdani’s résumé is comparatively slight. The son of a renowned filmmaker and academic, he bounced among gigs — working on one of his mother’s movies, as a rapper, a campaign organizer, a part-time tutor and a foreclosure counselor — before winning a seat in the Assembly in 2020. In Albany, he has a reputation more for advocacy than lawmaking.