It started being available in high-end cars in the late 1950's. Mid-60's it was a pretty common option, especially in the South. My '67 Malibu had factory AC. My dad's '66 Corvette does, too.
The systems were not as good as the modern blended air systems, but you can get upgrades from Vintage Air for most of the older cars. You'd get a much more modern AC system, using commonly available R134a, with a much better working defog/defrost setting, if you did the upgrade, and their kits typically use a control panel that looks like the factory units.
