The first recorded use seems to be by Stan Ulam in 1958, who was paraphrasing John von Neumann: https://ntrs.nasa.gov/api/citations/19940022856/downloads/19...

“One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.”

In the early 20th century, philosopher Pierre Teilhard De Chardin proposed that we are mentally evolving toward something transhuman and divine, but he didn't spell out a rapid transition. So the concept was sort of there, but von Neumann put it in a technological context.