It is hard to define the first superhero costume, as often there are characters who may or may not be considered superheroes who wore notable costumes. Prior to superheroes were pulp hero, an many of them wore costumes and disguises, in order to protect their secret identities.
Though he did not wear a costume, the character known as the Scarlet Pimpernel would inspire many characters who would, as he kept his identity by both being elusive and unseen, as well as a master of disguise. Zorro was a character directly inspired by the Scarlet Pimpernel and like the Pimpernel had an alter ego. However, unlike the Pimpernel, Zorro needed to act in public, so created not only his dual identity but also his costume to avoid suspicion. He was often presented in all black with a black mask to conceal his true face.
This fashion of heroes wearing disguises and having dual identities continued with such iconic pulp heroes as The Shadow and The Spider. In many cases they wore heavy coats, hats and masks of some sort to hide their faces. In other cases, the character may simply have an iconic outfit and/or look that remained associated with them., such as Doc Savage's white shirt and kahki pants.