At the age of 14, he was admitted to the Cologne Conservatory as a student of violin and composition, where he counted composer Engelbert Humperdinck as one of his teachers and conductor Willem Mengelberg among his classmates.

In 1895, Stock met with Theodore Thomas, founder and first music director of the then fledgling Chicago Symphony Orchestra, who was to have a decisive impact on his future.

That year, he wrote a symphonic poem Eines Menschenlebens Morgen, Mittag und Abend, dedicated to "Theodore Thomas and the Members of the Chicago Orchestra.

Under Stock's direction, the Chicago Symphony became one of America's top orchestras, developing a distinctive brass sound already heard in its first recordings.

An enthusiast of modern music, Stock championed the works of many then modern composers including Gustav Mahler; Richard Strauss (who, at Theodore Thomas's invitation, had been the CSO's first-ever guest conductor on subscription concerts in April 1904); Igor Stravinsky, whose Symphony in C was commissioned for the orchestra's 50th anniversary; Sergei Prokofiev, who was soloist in the world premiere of his Third Piano Concerto in Chicago (although he recorded it in 1932 with the London Symphony); Gustav Holst; Zoltán Kodály, whose Concerto for Orchestra was commissioned by Stock; Nikolai Myaskovsky, whose Symphony No.