Hussar
Legend
Not possible? I think that's a bit extreme. I mean, look at The Keep on the Borderlands or the Village of Hommlet. There's things going on, but really you're just poking around looking for the adventure- be it the Caves of Chaos or the Temple of Elemental Evil.
I'll admit there's more story to the ToEE, of course. But lots of early adventures are like "for whatever reason, you're here. Go look around!"
But even something as incredibly bare bones as KotB still has a strongly implied story. Your characters are going to go to the Caves. There really isn’t anything else to do except go to the caves.
As well, KOtB is set up for Basic DnD play which specifically tells you “go to the dungeon”. There’s no game if you don’t.
And even then the caves are set up with story. This tribe hates that tribe but is allied with the other tribe. That’s story right there.