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.
When Martha is suggesting names for Clark she says Christopher as an option, Christopher Reeve played Superman in many of the film adaptations in the 70s and 80s.