The first known use of "OMG" is from a letter written in 1917 from a British admiral to Winston Churchill.
Letters of Note curator Shaun Usher has pointed out what might be the first known usage of O.M.G., in a September 1917 missive from British admiral John Arbuthnot "Jacky" Fisher (or Lord Fisher) to Sir Winston Churchill. In a letter to Churchill about some "utterly [upsetting]" World War I–era newspaper headlines, Fisher wrote, "I hear that a new order of Knighthood is on the tapis — O.M.G (Oh! My! God!)— Shower it on the Admiralty!!" To which we assume Churchill replied, "Oh Dear Fisher! I am laughing heartily out loud!!"
There is nothing new under the sun.