Alaniz, an aspiring social worker, did not meet Sotomayor on Wednesday. But she and other first-generation and Latino teens were Sotomayor's focal point as the justice answered a series of questions culled previously from online submissions.
"Never give up on yourself," Sotomayor told the audience of about 5,200. And, if you think you don't belong, she said, "bear in mind that you're really not that unusual."
Sotomayor added that she continues to feel out of place among top U.S. officials. "At the State of the Union, it's very surreal for me. Here are all these people who appear on television, and then there's little old me."
The justice scaled stadium stairs in an informal, 90-minute session, mostly ignoring her security team from the U.S. Marshals office and wedging into back rows to plop beside youngsters and chat about her love of sculpture and reading.
Tickets for the free public speech at the Huntsman Center had sold out weeks beforehand.
She waved off requests from moderator Christine Durham, Utah's first female Supreme Court justice, that she return to the dais.
"I'm gonna finish taking pictures with these kids," Sotomayor said, posing for a photo.
The justice addressed topics ranging from how she manages to separate her own views from the law she is required to protect — "I have faith in the legal system." — to how she regards her Puerto Rican heritage — "You are a product of your family, their history and the riches that they can give you."
She counseled students to find mentors, ask lots of questions and seek to understand other points of view.
But the conversation stayed largely personal. Sotomayor avoided addressing gay marriage or any issue before the nation's highest court. Such questions would have been filtered prior to the event.
In her book, Sotomayor, recounts growing up in the Bronx with an alcoholic father who died when she was 9 years old, her spunky grandmother and dedicated mom.
She became the first Latina and the third woman justice when President Barack Obama appointed her in 2009.
As a kid, she had juvenile diabetes and learned to give herself the insulin shots. Her drive to be a lawyer, inspired by Nancy Drew and television characters, led her from high school valedictorian to prosecutor to judge.
On Wednesday, University of Utah President David Pershing looked on, smiling, as suited guards trailed Sotomayor up the stands.
"The thing that you just cannot help but see — she just excites the students," he said. "She's a wonderful role model," especially for first-generation students.