One reason that Gilgamesh is such an epic hero would reside in his mere birth. Gilgamesh was described as ""Two thirds they made him god and one third man." This enables him to be perceived as more than a man, but not quite an immortal. The next best thing would be an epic hero, someone who is ca.pable of great feats and inspiring actions. In this, one sees how Gilgamesh is an epic hero. Feats such as defeating Humbaba and the Bull of Heaven immortalize him. These actions are what contributes to Gilgamesh's condition of being an epic hero.
At the same time, Gilgamesh's condition is one in which he comes to understand truths about what it means to be human. He experiences pain, misunderstanding, and the all too coonstruction of mortality.