* Dr. Occult: He technically debuted in "The Mystic Comics" #5 (January 1938), published by National Allied Publications, which later became DC Comics. However, this was before the "DC" branding existed.
* The Sandman (Wesley Dodds): He appeared in "New Comics" #1 (February 1939), also published by National Allied Publications. This was before the "DC" branding existed, but the character's prominence and longevity make him a strong candidate for the "first DC character."
* Superman: He debuted in "Action Comics" #1 (June 1938), again published by National Allied Publications. Although appearing later than Dr. Occult, Superman's immense popularity and cultural impact make him a powerful contender.
Ultimately, there's no definitive answer. Depending on your definition of "first DC character," you could argue for Dr. Occult, The Sandman, or even Superman.