We can start by removing types of Pokémon for crystals that Ash didn't get.
1. We can rule out fighting types because the Fightnium Z was swapped. that means we can rule out the Crabrawleer line, the Stufful line, Passimian (if it were primary normal, then it might have had a chance), Marshadow, and the Jangmo-o line (as a fighting type).
2. We can rule out water types because Ash didn't get a Waterium Z crystal, that means we can rule out the Popplio line, Wishiwashi, the Mereanie line, the Dewpider line, the Wimpod line (as a water type), Pyukumuku, Bruxish, and Tapu Fini.
3. We can rule out the rest of the fire types because Ash didn't get a Firium Z crystal, that means we can rule out the Salandit line (as a fire type), Turtonator, Oricorio as a fire type, possibly altogether), and Blacephalon.
4. We can rule out ghost types (other than a possible Decidueye) because Ash didn't receive a ghostium Z crystal after taking what is basically the Ghst trial, this means we can rule out the Sandygast line, Mimikyu (for obvious reasons), Dhelmise, Lunala (as a ghost type, possibly altogether), Marshadow (again), and Blacephalon (again).
5. We can rule out dark types (other than a possible Incineroar) because the dark type Z Crystal was swapped, though Incineroar is the only dark type that is not an Ultra Beast.
We can also remove lines of pokémon that other characters already have, or for other reasons.
1. We can rule out all other Ultra Beasts, except Poipole, so no Nihlego, Buzzwole, Pheromosa, Xurkitree, Celesteela, Kartana,, Guzzlord, Stakataka, and Blacephalon.
2. We can rule out the major legendaries, so no Solgaleo, Lunala and Necrozma.
3. We can rule out the Piikipek line, because it's too late for Ash to get it (Ash usually catches the regional bird first, or second).
4. We can rule out the popplio line because Lana has Popplio.
5. We can rule out the Grubbin line because Sophecles has Chargabug.
6. We can rule out the Bounsweet line because Mallow has Stenee.
7. We can rule out Togedamaru because Sophecles has her.
8. We can rule out the Mareanie line because James has Mareanie.
9. We can rule out Mimikyu because Jessie has Mimikyu.
10. We can rule out the Stufful line because Bewear is with Team Rocket.
11. We can rule out Kamala because Principal Oak has Kamala.
12. We can rule out the Yungoos line because Officer Jenny of Melemele Island has Gumshoos.
13. We can rule out Orangaru because the only one we see works at a bar and had a focus episode.
14. Though Lurantis was a totem, it had focus, so that line's out.
15. We can rule out the Morelul line because that line had a focus episode.
16. Confey works at the Pokémon center, so that's out.
17. We can rule out Silvally because Gladion has Silvally.
18. No one can catch Minior because they die out once they lose their shell, so that's out.
19. We can rule out Drampa because Drampa had a focus episode.
20. We might rule out the island guardians because they protect the islands they're on (though I think Ash may (and I mean may) temporarily catch Tapu Koko).
21. We can rule out Zeraora because it will receive focus in a movie.
So after ruling out several lines and Pokémon, we are left with:
1. The Wimpod line (as a bug type).
2. The Mudbray line.
3. The Jangmo-o line (as a dragon type).
Alolan Ratatta line and Alolan Grimer line are crying in a corner.
I think we can rule out Wimpod as well, since i don't see Ash getting Buginium Z and Ash already has a Pokemon that acts like a baby in Poipole (I think they will depict Wimpod the same, since thats the whole gimmick around it)