I think SM/USUM are probably the best games, since it is possible to catch six pseudo-legendaries before the E4, even if it's only by a slim margin.
- Bagon can be found near the end of the first island (as pointed out by PX).
- In SM only, Deino can be found at Ten Carat Hill via Island on Tuesdays. Ten Carat hill is accessible on the first island once you get Tauros Charge (which you get after beating Hala).
- In USUM only, Larvitar can be found in Diglett Tunnel near the beginning of the second island.
- Goomy can be found in Lush Jungle via SOS in rain, near the end of the second island.
- Beldum can be found on Mt. Hokulani, which is relatively early on the third island.
- Gabite can be found in Haina Desert via SOS, near the end of the third island.
- And finally, the Kommo-o line can be found in Vast Poni Canyon, just barely squeezing in before the E4.
(and then Dratini can be found on Poni Island post-game, but we're not counting that).
Each game has 6 Pseudos littered throughout the game, several of which can be found relatively early. It's really down to a choice between Dieno (SM) or Larvitar (USUM).