It dawned on Sierra Moore, 24, who attended the protests carrying a homemade sign that read “No Justice, No Peace,” that she and her grandmother have been protesting the same issues over the course of a century.

She looked at the racially diverse group of thousands, which gathered for a short program on the State House steps before leading a march to the local police station.

Next to her was another sign: “Respect my existence or expect my resistance.”

“I just don’t think that’s how change happens,” Ms. Moore said of voting. “They’ve been telling us to do that for so long — and we’ve done it — and look at everything that’s still going on.”

Her words — expressing a sentiment shared by her peers — serve notice to politicians, civil rights groups and Mr. Biden, the presumptive Democratic nominee who has urged unity amid the frustration. “If you want change in America, go and register to vote,” said Mayor Keisha Lance Bottoms of Atlanta, but interviews with activists and leading Democratic figures including Stacey Abrams of Georgia, the longtime civil rights leader and former presidential candidate Jesse Jackson, and Representative Ayanna Pressley of Massachusetts, flipped that typical framework: If Democrats want people to vote, party leaders need to listen to why people are angry.