The listless Billy that we see throughout the duration of Slaugherhouse-Five is one that most likely is aware that his situation is “hopeless” in a sense that he’s incapable of changing anything that’s happening to him. Billy is aware that he’s in an “anti-glacier” (in reference to the quote about how trying to write an anti-war book is like trying to write an anti-glacier book; you’re going against something that’s impossible to get rid of) situation. I think one of the most independent decisions that Billy makes during the duration of the book is the decision to try and tell humans about his experiences on Tralfamadore. Upon his attempt at educating the world, he is called a fool by those closest to him, and dismissed as someone who is clearly crazy. If we’re taking Billy’s perspective throughout the novel at face value (which is easy enough, since this is a work of fiction), we know that he did go to Tralfamadore and his experiences are authentic. It’s possible that the message here is that it was fated that the rest of the human population wouldn’t know about the Tralfamadorians, and no matter how much Billy tries, he’s going to continually be met with confusion and doubt.
What counts as someone being a true “character” in the book is their ability to actually make decisions that attempt to go against what is going to happen, regardless of their decision. I’d also make a small case for Edgar Derby—when he stood up for what he believed in against the American Nazi, he was making a small attempt to change his fate. We know that he still ends up getting shot (after several reminders throughout the book), and even though he might not have been self-aware of his fate like Billy, it’s still notable that he made an subconscious effort to distinguish himself from other characters in the novel. Overall, I would say that the model Vonnegut uses--having characters with "free will" (not actually) operating within fate--was an interesting way to make readers question their own existence and what having free will really means.