As recently as the 1950s, it was accepted that half the population (the female half, of course) "should" be unemployed. Except they didn't call it being unemployed, they called it being a homemaker. We'll need big social changes, but changes like that have happened before. Hopefully we'll pull it off without causing too much pain to too many people.
A UBI would be a good approach. Not enough to replace working, just to reduce the demand for jobs. So more high school and college students decide they don't need jobs in addition to going to school. So more married couples decide they can afford to have one of them stay home and care for the kids. Then as the supply of jobs gradually decreases, you can gradually increase the UBI to try to keep the demand matched. I'm not saying it will be easy, but it's possible to do it without huge social disruptions.