Old-timey sci-fi writers John Wyndham, Charles Harness and Theodore Sturgeon saw the future as human evolution. In More than Human, Sturgeon saw evolution as not just the development of psychic abilities but also the creation of multi-person organisms, leading to the next stage of man, homo gestalt.
In one of my [many] favorite sci-fi novels, Nancy Kress's Beggars in Spain, there's a sort-of singularity (arguably it's not fast or profound enough, but it's the same idea) that's a confluence of three events: breakthroughs in human genetic engineering, the invention of cold fusion, and a popular new religion that preaches libertarianism.
Female authors Margaret Atwood and P.D. James envision a future where a failed ability to reproduce is the cause of massive change. I don't see futurism as a feminist issue, but they do suggest a different direction - and the paranoia that we won't wake up to the change until it's too late. I suppose you could translate that paranoia to the singularity idea by suspecting that aliens are already among us, changing things quietly under the covers. Or maybe we simply can't comprehend the change that's happening to us personally, as I can't differentiate my personal development from the societal changes happening during my childhood in the 60s and 70s.
In Stross's worlds a singularity is akin to an apocalypse: overnight society crumbles and most people die. That's not an event that people would fail to notice. (Unless it didn't happen in the northern hemisphere, or wasn't good at selling papers?)