The origin of the term "World War" (as opposed to "Great War") comes from the German "Weltkrieg," and the generic term "the World War" was common both during the war and after.

The specific terms "First World War" or "World War 1" were already floating around before 1939. One of the earliest instances that I can dig up is Lieutenant Colonel Charles à Court Repington's 1920 book "The First World War".

I came across this link a while back because I was interested in the same question. It's an interesting study of usage of term "World War 1" or "First World War" compared to "Great War."

Obviously, usage of "First World War" takes over in 1939, but there are several blips of usage before then. This study doesn't note the Repington book, though, because I don't think it looks far enough back.

In conclusion, the nature of the armistice in 1918 and the subsequent Versailles peace appear to have forewarned enough astute observers that the Great War was not the war to end all wars (and in many ways had the potential to be the opposite). Edit: See below for a better discussion and interpretation of this.

I'm interested to see if others have more examples of "First World War" or "World War 1" usage before 1939, particularly in cases coming from other languages. I remember reading that the term "Der Erste Weltkrieg" ("The First World War") was used as early as the during war itself, but can't for the life of me find the source.

Hope that helps answer your question!

Edit: I'm a professional editor but still can't do grammar, apparently.