A quick search shows an early reference to athletes taking simple courses such as underwater basket weaving in the LA Times of June 4, 1956, p. A4, "College 'Pro' Football Hit". It's an opinion piece about professionalism in college football. The author talks about underwater basket weaving and the preparation and serving of smorgasbord as "majors" that athletes have available to them. There's another opinion piece from June 10, 1957, p. B4 that mentions it. This indicates to me that it was in use in the vernacular at the time. This doesn't answer your question specifically but it gives a time reference to when it was seemingly in common use.

Too bad the 1956 letter to the editor of the Los Angeles Times is behind a paywall, but it described college athletes as "majoring in underwater basket weaving, or the preparation and serving of smorgasbord, or, particularly at Berkeley, the combined course of anatomy and panty-raiding."

Reed College has a holiday called Paideia. It's held before the first week of the spring semester, and it is a week of 'learning for the sake of learning'. During that time, professors, alumni, and students can all offer to teach courses on whatever subject suits their fancy. Two traditions of Paideia are Underwater Basket Weaving(which has been offered since 1984), and the Spotted Toad Speech competition (which is a Bio-Chem department challenge to make the most hilarious scientific abstract which still seems plausible to laymen).

This tradition of Paideia is a time honored inside joke about Reed itself, which still insists upon teaching a curriculum of a classical liberal arts education, including western humanities. The joke is that a liberal arts education is as useful as underwater basket weaving.