As dramatic music swirled late Monday evening, the woman trudged a few steps pushing a filthy shopping cart — so hunched and bedraggled that she seemed like an extra, sent onstage to set the scene before the star entered.

Then she opened her mouth, and a note emerged so pure and clear, widening into a cry before narrowing back into a murmur, that it could only be the soprano Lise Davidsen, cementing her stardom in a new production of Verdi’s “La Forza del Destino” at the Metropolitan Opera.

In her still-young Met career, Davidsen has triumphed in works by Tchaikovsky, Wagner and especially Strauss. She has quickly become the rare singer you want to hear in everything. But Verdi and the Italian repertoire traditionally belong to voices more velvety and warm than hers, which has the coolly powerful authority of an ivory sword, particularly in flooding high notes.

There were moments on Monday that wanted a soprano more fiery than ivory. Davidsen is statuesque, and her sound is too: grand and decorous. There were moments when the anguish of Leonora, the heroine of “Forza,” would have been more crushing if her lower notes had earthier fervor.

But come on. Quibbles aside, there are vanishingly few artists in the world singing with such generosity, sensitivity and visceral impact.