I didn't start my career until the late 90s but I never saw anyone write a unit test until the XP craze started kicking off in the early aughts. Even then it was a few more years before I saw it happen commonly.
Sure, we had regression tests at my jobs back then but they were always written and managed by QA groups. I never saw nor wrote any until a few years later.
I happen to have on my shelves Jon Bentley's More Programming Pearls. In the chapter "Bumper Sticker Computer Science" is the passage
'"It takes three times the effort to find and fix bugs in system test than when done by the developer. It takes ten times the effort to find and fix bugs in the field than when done in system test. Therefore, insist on unit test by the developer."
There is some OK stuff in here but there is also a lot of codswallop and it's far too verbose, eg. make sure you learn Node, be sure to read this set of books. "But everything old is new again, and ignore fads!" It's worse than verbose and of dubious quality, it's internally inconsistent.
Really, now.
The Unit Test wikipedia page cites as one of the external refs this:
IEEE Standard for Software Unit Testing: An American National Standard, ANSI/IEEE Std 1008-1987
The last four digits there refer to the year. I.e. Unit Testing had already crawled into a standard and died ten years before 1997.