Your question really is more of a linguistics question than a historical one. There is a broad pattern across a large number of the world's languages to have an interjection signaling for someone to be quiet, and typically it follows a similar pattern. These sounds tend to come from a class called sibilants, which are very strident sounds made by restricting airflow with the tongue. In English, our s, sh, and ch sounds are all examples of sibilants. Compare how loud you can make these sounds with sounds like f or th. Essentially, if you want to easily cut through a noisy environment, sibilants will get the job done.

This wikipedia page has a number of examples from various world languages, but they almost universally use some sort of sibilant sound. These languages come from many different parts of the world and language families, so using an interjection with a strong sibilant appears to be a natural linguistic phenomenon, not something inherited. In light of this evidence, the answer to your question seems to be that shushing has always been acceptable for telling someone to be quiet, perhaps going back to the origins of human language itself. Now, that doesn't necessarily mean that it has always been seen as polite, and even today there are some situations where shushing someone can seem quite rude. But its existence as a social practice appears to go far beyond the historical record.

As a librarian this question intrigues me, because I have a whole repertoire of shushes. I've consulted the Oxford English Dictionary, which has "shush" going back to 1925 (with one notable use being in Edna Ferber's 1929 novel Cimarron). But shush is an alternate form of hush, and hush goes back to the 16th century, with a notable use being Viola in Act 5 Scene 1 of Twelfth Night remarking "My duty hushes me.". The OED notes that "hush" derives from Middle English words like "hussht", with a notable use being in Chaucer's Canterbury Tales (The Knight's Tale).

My Latin textbook in highschool (Cambridge purple book, I think the 4th iteration of their program) had "sst" as an interjection being the equivalent of the English "shh," so I would say it's thousands of years old.

As a follow-up question does the shush we use to tell others to be quiet and the shush we use to comfort babies come from the same place?