Growing up in Harlem during the 1980s crack epidemic, Alvin Bragg said he once found a homicide victim on his doorstep and was threatened with a knife to his neck. At age 15, he said he was stopped by police officers at gunpoint, searched and then let go without explanation.

Those experiences are now at the center of his campaign for Manhattan district attorney. Mr. Bragg, who would be the borough’s first Black top prosecutor, has campaigned as the candidate who understands both the challenges of law enforcement and how the criminal justice system affects communities of color. Mr. Bragg said his platform speaks to issues he has seen affect the Harlem community where he has lived all his life.

“My election will not only be a symbolic change to the face of the office, but it will bring the perspective of someone who has lived their whole life in an impacted community,” said Mr. Bragg, a former federal prosecutor, deputy attorney general and civil-rights lawyer.

Mr. Bragg, the only Black candidate, has emerged as a front-runner in a historically diverse field of candidates seeking to succeed Manhattan District Attorney Cyrus Vance Jr., who isn’t running for a fourth term. The position has been held by two white men—Mr. Vance and Robert Morgenthau—for the past 45 years; only one white man, Assemblyman Dan Quart, is running this year in a Democratic primary field of eight.

The June 22 Democratic primary will likely produce the winner of the November general election in Manhattan, where Democrats outnumber Republicans by about nine to one.

Mr. Bragg, 47, has amassed a coalition of support anchored by his Harlem base. His supporters include Harlem heavyweights Rev. Calvin Butts and former Congressman Charles Rangel.

He has also tried to broaden his appeal beyond Harlem, reeling in endorsements from U.S. Rep. Jerrold Nadler of Manhattan’s West Side, former U.S. Attorney for the Southern District of New York Preet Bharara and the powerful service-workers union, 1199 SEIU. He has more Manhattan donors than any other candidate, according to January campaign filings.

His campaign follows a playbook that has propelled other Manhattan elected officials, like C. Virginia Fields, who became the first Black woman to win the borough presidency in 1997 by starting with a strong Harlem base and branching out from there. Other former Manhattan borough presidents Scott Stringer and Gail Brewer also drew on a strong geographic base in the Upper West Side in crowded primaries.

In a race with almost no independent polling, Mr. Bragg’s diverse coalition sets him apart in a divided, multicandidate election that needs a big-tent coalition, said Ms. Fields, who has endorsed Mr. Bragg.

“He’s the only candidate who is showing that level of broad-based support,” she said.

The election is unfolding amid a rise in shootings in New York City. Mr. Bragg said he would make gun-trafficking cases a priority, cutting off the source of the weapons and wouldn’t use a one-size-fits-all approach to gun prosecutions. In cases of simple possession, where a firearm isn’t used or discharged, he said not every person charged is driving violence and harsh sentences don’t always advance public safety.

“We have to address the flow of guns and the use of guns,” he said. “But we also have to know that not every gun case is the same.”

Mr. Bragg is a proponent of alternatives to incarceration and has released a list of lower-level crimes he would decline to prosecute. He has said he would improve programs for prisoners re-entering society, work to reduce mass incarceration and create an independent unit to investigate police misconduct.

“We can’t be safe unless we have justice and trust in the system. People try to make it a choice between the two, but I know from life that they are linked,” he said.

As a Manhattan federal prosecutor, Mr. Bragg took on public-corruption cases. At the attorney general’s office, he served as the chief deputy attorney general in charge of social justice and later became first chief deputy under both Eric Schneiderman and Barbara Underwood.

At the attorney general’s office, Mr. Bragg oversaw a unit that investigated police-involved deaths of unarmed civilians. By the time Mr. Bragg left the office in late 2018, his team had opened more than a dozen investigations. In every case, the division issued a report explaining charging decisions and made recommendations for systemic reform in all.

The division’s work has come under criticism for not securing any convictions. Two high-profile cases Mr. Bragg oversaw went to trial and resulted in acquittals.

At a televised debate Tuesday, candidate Lucy Lang asked Mr. Bragg why Manhattan voters should trust him to hold police accountable when he “repeatedly failed to do so when given the opportunity.”

Mr. Bragg has said the not guilty verdicts were some of the most painful moments of his legal career. Since then, he has continued working to change the law to reduce the obstacles prosecutors face in winning convictions against law-enforcement officers. New York was the first state to appoint attorney general special prosecutors to these types of police homicides. Other states have subsequently followed the model.

“There’s no shame in an acquittal. You bring the cases that you believe in,” said Mr. Bragg.

Mr. Bragg’s supporters say his life experience could transform an office that has been criticized for treating the wealthy and powerful with deference.

ReNika Moore, a former bureau chief who worked with Mr. Bragg at the attorney-general’s office, said he strategized with her about making sure people of color in low-wage jobs felt comfortable coming forward to report labor-standards violations. The people were often immigrant workers and feared retaliation, and Mr. Bragg ensured they knew hourly wage laws applied to all workers regardless of immigration status.

“He was able to wear many hats,” Ms. Moore said, which speaks to his ability to build a coalition from multiple constituencies.

Mr. Bragg said his experience growing up in Harlem made him realize that the criminal justice system needed to be reformed. He said he attended Harvard Law School, after graduating from Harvard College and the elite Trinity School on the Upper West Side, with the vision of marrying public safety with fairness.

When Mr. Bragg speaks to victims of violent attacks, he said that he thinks about the homicide victim on his steps and a knife to his neck. When he interviews a police officer, he thinks about the unlawful stops he suffered.

“I bring these experiences in everything I do,” said Mr. Bragg.

Write to Deanna Paul at deanna.paul@wsj.com

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