No, I think the closest was when the Colorado Rockies made the playoffs in their third season in Major League Baseball.
(Except, of course, in the first year of a league, when they’re all first year teams.)
When the nhl added six teams to the original six in 1967 they created two conferences. One held the o6 teams Montreal, Chicago, toronto, Boston, Detroit and the New York Rangers the other held the expansion teams. The playoffs were held by conference. So the St. Louis blues ended up plauing in the SCF that year, and three other teams made the playoffs. Not the same as the knights this year obviously but still officially playoff teams