"Seal Team 6" has become synonymous "elite". Is there a more generic term that can be used to describe a group considered the best at something?
Several things come to mind: Expert, maven, guru, and par excellence to name a few. Also, there's "the best...", as in "the best doctor" or just by itself.
Back in the old days we used to use the name "Heifetz"---after Jascha Heifetz, considered by some to be the best violinist that ever was:
"He an ok ball player, but he's no Heifetz".
and my favorite variation:
"You are either Jascha or kasha."
(Kasha is boiled buckwheat.)
"Seal Team 6" is an EXAMPLE of an elite group. I've never heard it used as a generic term for an elite group. Maybe among your friends and associates people say, "This band is the Seal Team 6 of rock stars!" or some such. If so, I think that usage is very localized.
But in general terms for a person or group who are the best at something include, "elite" like in your question, "premiere", "the best", "A-team", and "first string".