Beowulf: Fake or Fiction?

While I was reading this epic poem, this revered and historical journey, I couldn't help but feel that Beowulf just wasn't real. Maybe it's because I'm not an Anglo-Saxon myself, and I never will be, but I just cannot imagine someone having that much bravery; that much loyalty to his king. Beowulf's descriptions of King Hygelac are almost as if he is describing the Almighty God or some other superior being. It just seems so...fake. Unnatural. I must say, the monsters certainly did not make the story any more believable in my eyes. When Grendel is mentioned to be "loping" towards Heorot, I can't help but imagine this scaly, green (I'm not sure why, but maybe because he lives in the swamps, I imagine him to be green and covered in nasty goo) creature, somewhat hunched over with uneven arms and legs, galloping towards the glittering hall of unity. It just doesn't seem real to me.
Sure, I admit that this poem was written for entertainment, and fantasy is allowed, but shouldn't the main character at least have more real human-like characteristics? I don't know that many people who would willingly take on a vicious monster with his bare hands, or dive underwater to kill a monster, and come up with another monster's head. Beowulf doesn't seem to be a real person, or even a hero; rather, he seems to be the ideal warrior, the legendary man that every little boy wants to grow up to be and every little girl wants to grow up and marry. He is too brave, too sure of himself, too much of an archetype of Anglo-Saxon society for him to be believable to me. Perhaps it is that I am not quite getting the grasp of what an epic hero is.
On the other side, I have found some more human-like and less god-like characteristics about Beowulf, especially as he gets older. He seems to have finally learned that he is not as strong as he once was, and brings his thanes with him. He understands he needs weapons in battle. He is ready to truly face death. However, I can't quite say this is a coming of age story, because Beowulf never really reaches that mature level of understanding that comes from a coming of age. He is not like the young girl who climbed the tree and saw the vast ocean in front of her. He is not like Edna, who finally sees the futility of her rebellion against society. I guess what I'm trying to say is there is no epiphany, no AH-HA moment. And I guess that's what made Beowulf so unreal to me. My belief is that in life (and in literature), almost all characters have that one moment of discomfort, of that feeling that something isn't right, and they move towards a goal: fixing that discomfort, whatever it may be. Maybe I'm missing something here, but Beowulf just seems...too epic to be real.