Short answer: Tarzan movies

Discussion:

The first reference I find to quicksand, albeit in metaphor, is in Spenser's The Faerie Queen [1590]

But by the way, there is a great Quicksand,And a whirlepoole of hidden ieopardy, Therefore, Sir Palmer, keepe an euen hand; For twixt them both the narrow way dothly. Scarse had he said, when hard at hand they spy That quicksand nigh with water couered; But by the checked waue they did descry It plaine, and by the sea discoloured: It called was the quicksand of Vnthriftyhed.

This seems consistent with the idea of quicksand as a hidden danger (given the context I take "the quicksand of Vnthriftyhed" as the "quicksand of unthrifty-ness"); so Spenser must have been confident that the imagery would be familiar to a reader, that quicksand could evoke the same kind of viscous panic overwhelming that we use when we say "mired/drowning in debt".

It then seems quiet again for "quicksand" for some centuries -- most of the references you'll find are to issues in masonry and roadbuilding, not the same thing. But in the 18th century, you see it in Samuel Johnson's The Rambler, in the dramatic sense: "narrowly escaped suffocation in quicksand"; but most of the references are less dramatic, discussions of wagons or cannon mired in quicksand-- eg practical, not melodramatic.

It's in the 19th century when Europeans tell tales of adventure and exploration from the tropics that you start to see it in the Indiana Jones sense of a jungle peril. It shows up a lot in accounts from India, in British periodicals like Chamber's Journal, but again, it's still more practical than "if you step on it, you'll be sucked in, in an instant".

The Hollywood trope can be specifically identified with one particular movie: Tarzan, I think specifically the 1936 film, Tarzan Escapes. Quicksand was a mildly interesting literary metaphor, but it was great on screen-- so notwithstanding Spenser's rather poetic use, our melodramatic sense of quicksand comes from the movies, and is less than a century old.