I’m afraid prepared foods and drinks don’t always have the sort of etymological provenance you seem to be seeking. When was the verb squash first used as a noun to denote a drink? A quick search of Google Books shows the earliest literature mentioning squash is The Adventures of Cooroo, a Native of the Pellew Islands from 1805. From a glance it appears to be known as an alcoholic drink at the time, and is mentioned without explanation so it was part of the popular lexicon and could have been used for years before that.
From there it morphed into your aforementioned “lemon squash” in the late 1800s, which seemed to be a nonalcoholic drink made from crushed lemons and soda water. By at least 1897 recipes for squash mentioned “essences” of lime- and lemon- squash so it is easy to see that transitioning to the sweet flavored syrup by 1938 when Ribena first produced your Blackcurrant Squash.
It becomes even more murky when you search for cordial, which appears much earlier and also denoting an alcoholic drink(Although cordial seems to have first had a more medical use).
If you are going to pose the question to a more academic circle I’d advise specificity. “When was the word ‘squash’ first used to denote a beverage?” is a good question, or even “How did squash turn from an alcoholic drink to the nonalcoholic drink base we know of today?”; My uneducated guess is the temperance movement may have had a hand in that.