Geeta's team would be the easiest to build.
All of her team members are readily obtainable in both Scarlet and Violet before defeating the Elite 4 for the first time, without the requirement to trade or bypass post-game exclusivity. Her team also has no Egg or Tutor moves. All other Champion teams have post-game or trade-only Pokemon, items, and/or moves.
Blue has version exclusives, trade evolutions, and Pokemon found in the Safari Zone, in all three games.
Lance has Pokemon that are unobtainable in both generations in which he is Champion, namely all three underleveled Dragonite. In Gen 2, Charizard and Aerodactyl are unobtainable without trading with Gen 1.
Steven, Wallace, and Cynthia have multiple of the same TM move, which you can only normally obtain once, necessitating breeding and/or trading. Cynthia ramps this up with Egg moves on some of her Pokemon, as well as with a large portion of her team being difficult to obtain (Spiritomb notably requiring another game to obtain).
Alder is a post-game fight, so very little is gated away. The only restrictions I can see are the two trade evolutions on his team.
Iris has Archeops, which is post-game only. Her team also has many Dragon-types and pseudolegendaries that are difficult to level up.
Diantha's Gardevoir is holding Gardevoirite and has Shadow Ball, both of which are post-game only. She also has both fossils, while you can only pick one.
Kukui has a version exclusive to Sun, and a starter you didn't pick. Hau has the latter, as well as a BP move.
Trace has Vileplume, a Let's Go! Pikachu exclusive. He also has Pidgeotite, which is post-game only, a restriction that cannot be bypassed as LGPE lacks held items.
Leon has a starter you didn't pick. Also, if you picked Grookey, his Seismitoad has an Egg move.
BDSP scales back the complexity of Cynthia's team's movesets and makes Spiritomb and Milotic more reasonably obtainable, while also giving every team member a held item. Her Milotic has a Flame Orb, which is post-game only.
(Fun fact: I had spent a few hours typing out detailed explanations for each Champion and their team members to answer this question with detailed analyses, but I hit the character limit and could not reasonably trim it. I may make the detailed explanations available elsewhere, perhaps on Pastebin?)
