What is the origin of the slang term "get out of here" to mean "you're kidding"?

Solution 1:

This term may have originated from several places.

First, the sport of baseball.

The usage may have come from: "It's outta here!" that was used during the occurrence of a home-run. From this basis and with the help of the radio, this terminology might have caught on. Anything that seems out of the ordinary was deemed 'out of here' and when a tall tale or something mind-boggling was stated, the term must have spread.

There are numerous phrases that have originated from sports that we use today, and this could be another one of those.

Second, from a person about to be fired telling a tall tale or making a elaborate excuse to keep his job.

This might have evolved during the stock market crash of the 1920 where jobs were starting to get hard to come by and the country was on its way to it poverty stricken status of the 1930s. The boss might have listened to story after story and told each one to 'get out of here', which might have led to this statement being what it is.

Third, is has been adopted from a foreign dialect. Spanish is the most likeliest as they have an expression that translates quite nicely, specifically ¡vamos! which is now adopted into the English vocabulary as vamoose.

Fourth, really bad books. There is a book called Gus the Bus and Evelyn, the exquisite checker published in 1917 that uses this phrase in its literal form. It implies that the person is nutty (see image below).

Fifth, Vaudeville. The stage was a place where all sorts of people could watch all sorts of plays, acts, etc. Bad acts were told to get off the stage, which lends to the whole (in)famous Vaudeville Hook shtick. A bad act was considered outrageous because it was a waste of time and money for the audience. This could have evolved from this point to mean that something is outrageous (as in a tall tale).

Again, these are all speculative answers and I cannot find enough concrete evidence to fully throw in with one or the other.

Solution 2:

I'm not sure about the origin of the phase, but in chapter 12 of "The War of The Worlds" by H.G. Wells, a character identified as the lieutenant says "get out [...] what confounded nonsense" in response to a description of the Martians. This book was published in 1898 making it a very strong contender for being the first recorded of the saying.