The epiphany in this story to my mind comes when George realises that there is only one way that this could end, and this is when he finds Lennie in the place where he told him to hide in case there were any problems at the beginning of the story. George experiences a sudden epiphany that is incredibly tragic. He realises that the best thing he can do to help Lennie is to kill him as painlessly as possible himself before the other men get to him and he is probably lynched. However, at the same time, this epiphany makes him realise that his and Lennie's dream of companionship together and facing the troubles of the world as a team is completely over, and George will become the kind of man that he has prided himself on not being because of his friendship with Lennie. Remember how George describes normal "guys" who work on ranches in the first section of this story:
Guys like us, that work on ranches, are the loneliest guys in the world. They got no family. They don’t belong no place... With us it ain’t like that. We got a future. We got somebody to talk to that gives a damn about us. We don’t have to sit in no bar room blowin’ in our jack jus’ because we got no place else to go. If them other guys gets in jail they can rot for all anybody gives a damn. But not us.
With the realisation that George must kill Lennie comes the realisation that he will end up just like one of these "guys" that he never wanted to be in the first place.