Last Friday evening, Zohran Mamdani, sweaty and grinning, began walking south from the northern tip of Manhattan as part of a final push for votes in New York City’s fiercely contested Democratic mayoral primary.

Mr. Mamdani, a Queens-based progressive state assemblyman, strolled down from Inwood Hill to Battery Park, his campaign shooting video along the way. He hugged a bicyclist. He dapped up a man outside a bodega. He ate a slice of pizza.

In other words, he looked like a normal human being — albeit one who was on a 13-mile walk in the middle of the night.

In the months since their loss to President Trump last November, Democrats have been engaged in a prolonged period of hand-wringing and soul-searching, seeking answers for how to win back the voters who said the party had lost touch with them and catered too much to elites. Strategists and focus-group researchers proposed one seemingly simple fix more often than anything else: Just be yourself.

In New York, Mr. Mamdani embraced that strategy. Through slick social media videos and an army of thousands of volunteers, he defied conventional political wisdom about how to win a citywide race in a deep-blue city.

He has also offered national Democrats still licking their wounds after bruising losses last November a test case in re-energizing voters. The 33-year-old democratic socialist ran an unorthodox campaign that seemed to catch lightning in a bottle, surging from little-known statehouse politician to late-stage front-runner alongside a more accomplished rival, former Gov. Andrew M. Cuomo.