At least in the late 70's - early 80's, if you could find an employer to "sponsor" you (basically agree to give you a job for a certain amount of time), then you could immigrate with a green card immediately. There was no specific "scheme" for particular occupations: many of the people who did this were low-wage workers doing housekeeping, janitorial work, construction, etc.

I'd assume something similar was already in place during the 60's.