A bit of history first: the original expression, of course, was I couldn’t care less, meaning “it is impossible for me to have less interest or concern in this matter, since I am already utterly indifferent”. It is originally British. The first record of it in print I know of is in 1946, as the title of a book by Anthony Phelps, recording his experiences in Air Transport Auxiliary during World War II. By then it had clearly become sufficiently well known that he could rely on its being recognised. It seems to have reached the US some time in the 1950s and to have become popular in the latter part of that decade. The inverted form I could care less was coined in the US and is found only there. It may have begun to be used in the early 1960s, though it turns up in a written form only in 1966.