A good deal of inspiration was drawn from the recent online enthusiasm for West Marches-style campaigns (a more intentional and well thought out way of running the kinds of campaigns we ran back 20 years ago in teen years). We essentially had no prefigured plotline in place at the start. The campaign setting was limited to three paragraphs and I tried to pare back all the over-deterministic world-building impulses to a minimum.
Taking a different tack, I sketched out a good old-fashioned sandbox complete with a hand-drawn players' map highlighting a number of obvious dungeons (two big ones and several smaller ones), numerous vaguely-defined points of interest, and a handful of civilized habitations. After handing over the map, I explained that they were free to explore, but that the encounters would not be scaled to be totally appropriate to their level. If they ignored the obvious warning signs of an area above their heads then it fell on them to figure out how to get themselves out.
Interestingly enough, as nature abhors a vacuum, a vague storyline is seeming to develop from the bottom up as the play sessions unfold. Players have started to ascribe meaning and patterns to the characters, monsters, histories, sites, and events (the moving parts behind the scene) they discover--and a player-centered "plot" begins to be born.
You can check out some other interesting examples of the thinking behind sandbox-style games on the links below:
How to Set Up a Sandbox Campaign
Old Schoolin' How to Get Started
Cautionary Tales from the Sandbox