SAN ANTONIO — Julián Castro, in a baseball cap and zip-up hoodie, sipped an iced tea and considered how he could win the Democratic presidential nomination.

“If everybody would just get out of the way,” he said on a recent afternoon, “I’d have a clear path.”

He was only half-kidding.

Mr. Castro is in need of a breakthrough moment. Once considered a rising star in the Democratic Party — he was the first Latino to give a keynote address at the Democratic National Convention — he has been outshined in the ever-expanding field by brighter stars and nonstars alike. While he has many fans in his hometown, San Antonio, where he once served as mayor, he is not well known on the national stage. And with the sudden rise of the former El Paso congressman Beto O’Rourke, Mr. Castro is not even the most well-known candidate in his own state.

Still, during an interview at one of his favorite Tex-Mex restaurants, Mr. Castro seemed relatively unfazed, and maybe for good reason: At age 44, and as the only Latino candidate in the race, he would seem to satisfy the Democratic Party’s desire for youth and diversity, to say nothing of strategists who view Hispanic turnout as an important factor in winning back the White House.