Who knows when it began, The Harlem Globetrotters were doing it as part of their routine in the 1940's and 50's, Cousy and Hot Rod Hundley were doing it on the regular in the NBA in the 50's into the 1960's and based on footage it seems almost every good player from the 60's and on would try it now and again even the unflashy ones like Jerry West I have footage doing it at least once or twice. The Globies and the few NBA players who were good enough not to cause a turnover and get benched while doing it regularly all brought it straight from the playgrounds. No look passes were probably being done on school yards and playgrounds since shortly after the games inception in the early 1900's for all I know but Cousy was probably the first huge name Pro/NBA superstar to make it well known outside of Globetrotter shows and of course you also must give the Globetrotter legends props like Goose Tatum and Meadowlark Lemon
Sorry no mixes of the first no-look passes lol but here's Sam Jones in 1966 on the Celtics mirroring a type of pass Cousy was doing on the team 10 years prior
Even "no names" like Bill Bradley here dishing to Willis Reed would do it. It didn't take a genius to figure out a no-look pass is an effective way of tricking defense - like I said I bet people on playgrounds and in company leagues did this very early in the games history. Every era I've seen that has lots of footage all have players executing "no look passes"
**EDIT** I didn't gif these myself, but looks like some people already noticed Cousy was a good passer, here's some of Cousy - it's not his best either, he did some mindblowing passes in footage I got but it's enough to show him do it
To young Wilt in an ASG