Given that the one Western characters in the base game and Fighter's Pass #1 are from Rare and Retro and are from first party or former first party games, I wonder if it's time to give up hope for a Ubisoft or Bethesda rep. Maybe not, since Ubisoft is getting Mii costumes in the next update, but it does seem like Nintendo/Sakurai are mostly sticking to characters and franchises that originated in Japan.
I also think a Gen 8 Pokemon is all but guaranteed in this Fighter's Pass, given the large number of Pokemon already in the game and the ridiculous success of Sword/Shield. It'll probably be the final form of one of the starters (Intelleon, maybe?) but I'm holding out hope for a Wooloo miracle. (I mean, Jigglypuff made it.)
Beyond that, I have no idea. There aren't that many new Nintendo franchises without reps. Labo wasn't successful enough to justify one, and is probably done. Arms did OK, but unless a sequel is planned I'm not sure Nintendo is interested enough in the IP to bother (especially since no Arms character made FP1). Ring Fit Adventure seems to have legs (har har), so ... maybe? I'm not sure the overlap is there with the Smash fanbase to incentivize sales of Ring Fit Trainer (or whatever she's called) as DLC. Dragaux would be hilarious, but is an even longer shot.
Rex and Pyra/Mythra seemed like obvious choices, but their absense from FP1 and the fact that Monolith has moved on to other projects and XC2 is past its prime sales-wise makes me wonder if the Rex Mii costume is all we're getting. (I still think there's a good chance this could happen though.) Given that Nintendso seems unwilling to even port XCX to the Switch, Elma probably has no chance. Ditto to Wonder Red for the same reason. Super Mario Odyssey is huge and probably will get a sequel eventually, so maybe Pauline has a real shot?
As far as third parties are concerned ... Christ, who knows? Master Chief seems like he has a real chance if Halo actually does get ported to the Switch. Travis Touchdown has to happen eventually, right? Sakurai has to take mercy on poor Suda51. The man has been begging for Travis in Smash since Brawl. Plus, Travis has appeared in three games on Nintendo systems with a fourth coming with one being a full exclusive (NMH2), two being timed exclusives (NMH1 & TSA), and NMH3 being either a full or timed exclusive, so he has a closer association with the Nintendo brand than a lot of the alternatives (not that it always matters, considering Cloud and Joker). But really, I have no idea. I would have never guessed that Joker or Terry would make it in FP1, and we don't even know if FP2 will have a substantial number of third party characters.