Surprised it didn't happen during the first expansion era, but I looked and it was only three consecutive Finals sweeps.
For those who don't know, when the Original Six expanded, they brought six new teams on board, and separated the divisions between new teams and old teams. So for 3 years in a row, an expansion team would make the Finals by default. More specifically, the St Louis Blues made the Finals 3 years in a row, and got swept all three times.
The divisions were only adjusted once Vancouver and Buffalo came into the fold (with Canucks getting put into the "East" for some reason??). Of course, as soon as Chicago got put into the expansion conference, they immediately made the Finals and lost a 7-game series to Montreal.
I think it's safe to say, with so much emphasis on parity, we won't see circumstances like that in our lifetime, and OP is probably safe to declare that it will never happen again. What's confusing me, is how people aren't understanding the premise of this thread lol