Link is explicitly revealed to possess the Triforce of Courage in The Legend of Zelda: Ocarina of Time (N64, 1998).
Near the end, when Ganondorf seizes the Triforce of Power and Zelda holds the Triforce of Wisdom, the Triforce of Courage resonates within Link—marking him as the chosen hero. The three pieces unite into the full Triforce during the final confrontation.
Ocarina of Time is the first game where the three-piece Triforce and Link's Courage piece are explicitly named and shown, establishing the mythology that defines the series.