Yes of course. Hercules, Perseus, Horus, Mithra, Baldr to name a few of the ones who walked the earth. Gods of war are considered heroes but they are immortal, and I would only consider "heroes" those who risk their life. But they are still many amazing warrior and miracle working deities throughout various cultures.
The Monkey King is based of Chinese myths, but it is still "based off" therefore not 100% truth. Much of it is fiction. Thor (as in the Marvel Comics) again is "based off" of authentic myth but is still fiction. I suggest reading into mythology. My favorite legends above all is the Arthurian legends. Now those are excellent reads and steeped in mythology.