Answer:
No one is certain when the phrase was coined.
Step-by-step explanation:
Webster the Marriam version (citing Hearst’s International - Cosmopolitan) states that it's earliest use dates as far back as 1929.
It is interesting to note that "I could care less" and I couldn't care less" are used as synonyms to mean that one is not overly concerned about a matter.
An example would be:
Tired and worn out, he sat up. ”I couldn’t care less,” he said, “whether you stay or not.”
Cheers