Kamala Harris, a California senator and daughter of immigrants who has broken racial barriers at every step of her political career, made US history on Wednesday night as she became the first Black woman and first Asian American to formally accept a major party’s vice-presidential nomination.

In the most consequential speech of her career to date, Harris urged voters to reject the divisive and destructive leadership of Donald Trump, calling him a president who “turns our tragedies into political weapons”.

“We’re at an inflection point,” the 55 year-old said, speaking from a waterfront convention center near Joe Biden’s home in Wilmington, Delaware.

“The constant chaos leaves us adrift. The incompetence makes us feel afraid. The callousness makes us feel alone,” she continued. “It’s a lot – and here’s the thing: we can do better and deserve so much more.”

Harris’s sister Maya, her niece Meena, and her step-daughter Ella Emhoff offered their praise of Harris as she was formally nominated, and her address introduced Harris to a nation still largely unfamiliar with the California senator.

Moments before she spoke, Harris stood at a darkened podium as a technician checked the sound. She took a deep breath. The cameraman counted down to zero and the lights above her illuminated.

Harris smiled: “Greetings, America.”

Born in 1964 to Shyamala Gopalan, an Indian-born American cancer researcher, and Donald Harris, an American economist from Jamaica, Harris recounted their political activism and said that some of her earliest memories were of attending civil rights protests as a toddler.

She described her family – both the one she was born into and the one she created – as foundational to her life and career, bringing some Indian-American women watching at home to tears with a mention of her chithis. Acknowledging the weight of nomination, she invoked her mother, along with the names of Black, female civil rights leaders who helped pave the way: “We all stand on their shoulders.”

“My mother taught me that service to others gives life purpose and meaning. And oh, how I wish she were here tonight but I know she’s looking down on me from above. I keep thinking about that 25-year-old Indian woman – all of five feet tall – who gave birth to me at Kaiser Hospital in Oakland, California,” she said.

“On that day, she probably could have never imagined that I would be standing before you now speaking these words: I accept your nomination for vice-president of the United States of America.”

In her remarks, Harris also delivered a biting rebuke of Donald Trump, or, as she calls it, “prosecuting the case” against the president of the United States.

She said: “Donald Trump’s failure of leadership has cost lives and livelihoods. If you’re a parent struggling with your child’s remote learning, or you’re a teacher struggling on the other side of that screen, you know that what we’re doing right now isn’t working.

“And we are a nation that’s grieving. Grieving the loss of life, the loss of jobs, the loss of opportunities, the loss of normalcy. And yes, the loss of certainty.”

Her speech threaded together the two major arguments Democrats have advanced across their four-day convention: that American democracy hung in the balance – and that voters must mobilize in historic numbers ahead of the November election to ensure not only that Trump is denied a second term but that Democrats take control with a governing mandate.

“It’s not about Joe or me. It’s about you. It’s about us,” Harris said. “People of all ages and colors and creeds who are, yes, taking to the streets, and also persuading our family members, rallying our friends, organizing our neighbors, and getting out the vote.”

“And we’ve shown that, when we vote, we expand access to healthcare, expand access to the ballot box, and ensure that more working families can make a decent living.”

As Wednesday’s event began, Harris gave a brief direct-to-camera speech about the importance of voting in November’s election. She said she knew many of the viewers may have “heard about obstacles and misinformation, and folks making it harder for you to cast your ballot,” offering implicit criticism of Trump.