The costume and name do not make the hero, the actions do
Nobody said he wasn't a hero from the start. But he wasn't Daredevil. Costumes and a name may not make a hero in a common English usage of the term, but they do make a superhero as the term is used in a comic book. Clark Kent was born with his powers, and helped folks when he was younger, but he doesn't become Superman until he's an adult. Matt Murdoch is the same; he becomes Daredevil in the last scene of the season.
It's an origin story for Daresevil and Kingpin. Origin stories in comic book terms aren't just how superheroes get their powers - it's how they begin their identity as a specific named, costumed superhero.
Sups 1978? It has been a while, it is a lot less of an origine story than Batman Begins. We get some stuff at the beginning and then he is a hero. Very different from the last Superman movie.
You don't see Superman in the first half of the film, just like in Batman Begins where you don't see Batman for the first half. In both movies, the titular costumed identity shows up over an hour in. The first half of each film is an origin story.