If we were to ask Rosie Cotton: "What do you think, how was Eä created?", what would she answer? To my knowledge every culture has a story on how the world began. Most of them are probably wrong, but if Rosie Cotton believes it was the music of the Ainur she would actually be right. So to me it seems more likely that she'd be wrong about it, because people are usually wrong about stuff like that (at least in the real world). So maybe she believes in the Big Bang (that naive nit!) or she thinks (like Einstein did) that the world has always been there.
I suppose Gandalf, Elrond and other highly educated people know the truth. But what do ordinary people believe? What are Balins or Grimas opinions on that topic?
I am aware, that there was no religion in middle earth. But still they must have a theory on how the world began. Even if they believe the right theory, and know about its divine origin, it wouldn't necessarily be an religious explanation. It could just be a well known fact, every child learns in 3rd grade in physics lesson.