Idk if I'm missing that term from some sort of guide or FAQ or whatever, but what do you mean by HAT group? Could help for newer players.

I'd also like to amend that I''ll be awakening Bashira as well before getting Saki. Archers and Healers seem to be the most important core classes and having two of each awakened as early as possible seems to be a big boon for G maps. I would also awaken another premium healer if I had access from Events or Shrine.