I believe OSD was introduced first for VCRs, then televisions, and computer monitors later. VCRs have had OSD since the early 1980s at the latest. Mid-1980s large-screen televisions also had OSD for channel selection, volume control, etc.
If you can find a photograph of a monitor, a sure sign that it has OSD is if it has up-down buttons but no LCD panel (some high-end CRT monitors had LCD parameter displays instead of OSD). An exception was screens like the AppleVision 14", which do have buttons but the controls were routed through the computer so OSD was not necessary.
My earliest monitor with OSD is a Sony workstation display from 1993. It also has a remote control.