Despite getting punched hard in the face during the alley-behind-the-Gaslight-Cafe scene in Inside Llewyn Davis, Llewyn's face is shown subsequently to be undamaged. No bloody nose, no swelling or redness on the side of his face at the end of the movie. So was that sequence a dream? Like many questions concerning the timeline and meaning of the scenes in the movie, it would be difficult to say where the reality and the dream separate, if there is a dream sequence in the movie. But, especially on the morning AFTER getting clobbered in the face, we should be able to see swelling on Llewyn's face. Once we see a repeat of the opening scenes in the last scenes of the movie, we realize that the morning the cat gets out is not the morning after Llewyn's Gaslight gig. Still, the closing scene should show Llewyn with some damage to his face from the fist of the big Arkansas fellow.
The unreality of that is like the unreality of Llewyn seeing the movie poster for The Incredible Journey, since the movie wasn't released until 1963 or '64. Using the literal meaning of "incredible," or perhaps its original meaning, which is "not credible," one interpretation of the seeing of the movie poster is that it is Llewyn's journey that is not credible. We know the seeing of the movie poster itself is not credible if we assume the year is still 1961 when he sees it.
Also we have the name Llewyn to compare to the name Llewelyn of the character in No Country for Old Men. I guess I'm like Larry in A Serious Man, who can't help feeling the questions. Why do the Coens make us feel the questions if they aren't going to give us the answers? To paraphrase Rabi Nachtner: "They haven't told me." That in itself, of course, is an example of a question without an answer.