He also conducted the first national tour of Carmen Jones and worked as an accompanist, notably playing for tenor Leslie Chabay in his New York City recital debut in 1950.

[3] Kozma made his conducting debut at the Metropolitan Opera House on January 4, 1951, leading a production of Johann Strauss II's Die Fledermaus with a cast that included Marguerite Piazza as Rosalinde, Set Svanholm as Eisenstein, Patrice Munsel as Adele, Eugene Conley as Alfred, and Jarmila Novotná as Prince Orlofsky.

He conducted a total of 82 performances at the house over the next six years, including performances of Modest Mussorgsky's Boris Godunov (with Jerome Hines and Nell Rankin), Georges Bizet's Carmen (with Risë Stevens and Richard Tucker), Ruggero Leoncavallo's Pagliacci (with Lucine Amara, Ramon Vinay, and Robert Merrill), Giuseppe Verdi's Un ballo in maschera (with Zinka Milanov, Jan Peerce, Roberta Peters, and Marian Anderson), Wolfgang Amadeus Mozart's Die Zauberflöte (with Theodor Uppman and Mildred Allen), and Richard Wagner's Die Meistersinger von Nürnberg (with Otto Edelmann, Albert Da Costa, and Martha Lipton).

His final assignment at the Met was on March 30, 1957, conducting Giacomo Puccini's La Bohème with Dorothy Kirsten as Mimì, Richard Tucker as Rodolfo, Laurel Hurley as Musetta, and Ettore Bastianini as Marcello.

[3] On July 1, 1954 he conducted a concert version of Johann Strauss II's Die Fledermaus at the Lewisohn Stadium with Lois Hunt as Adele, Regina Resnik as Rosalinda, Charles Kullman as Alfred, and Betty Allen as Prince Orlofsky.