Superman: The Last Son of Krypton

A throwaway line of dialog actually establishes that in this continuity, Bruce Wayne became the Batman before Kent went public as Superman; while Kent ponders adopting a costumed alter ego, Martha Kent actually refers to "that nut in Gotham". In most other continuities, Kent's emergence as Superman predates Bruce Wayne's emergence as the Batman since Action Comics#1 came out before Detective Comics#27 (the respective first appearances of Superman and the Batman). The Earth-1 Kent began his champion career as Superboy well before the Earth-1 Wayne became the Batman. However, two stories indicate that the Earth-2 Batman was active as early as 1937 (Detective Comics#65 and World's Finest Comics#60); since the first Batman story in Detective Comics#27 was not an origin story, this may indicate that the Earth-2 Batman began as an adventurer before the Earth-2 Kent became Superman.

Edited from Superman: The Last Son of Krypton: Part I (1996)