And a younger Alfred fits, because this show is toward the beginning of Batman's career. Note that Gordon is still a lieutenant instead of the commissioner.
Which makes this the second "young Batman" animated series; The Batman
also focused on his formative years. Whereas in the DCAU he'd been active for a considerable amount of time (B:TAS featured an 18-year-old Robin, and Bruce had already been Batman when Robin was 9), and in The Brave and the Bold
(and Young Justice
) Batman was an established veteran and a leader of the superhero community.