As far as chances are concerned, I think it's honestly a toss up between Byleth and Edelgard.
Byleth has de facto main character status regardless of route, and has a whip sword and time powers. However, they're also another sword lord, which even Sakurai has spoken to the perceived redundance of, and has little to no personality due to being Fire Emblem's only silent protagonist.
Edelgard brings an axe moveset (and Sakurai said he wished more characters used axes when discussing Piranha Plant in his column), had a major presence in Three Houses's marketing (she was the first character we got introduced to, she's getting a figma, she was the headliner alongside Byleth on the first Three Houses banner in Heroes, they had a professional cosplayer cosplay Edelgard at FE Expo, and Edge of Dawn is literally her theme), has a strong personality, and is important even in routes that aren't her own. However, she isn't the main protagonist in every route, unlike Byleth.
Dimitri would bring in a lance moveset and is INCREDIBLY popular, especially in Japan. However, his popularity likely came too late, and may not outweigh the fact that Dimitri isn't as important to all routes as Byleth and Edelgard are.
Claude...I adore Claude, and of these four he's my most preferred choice after Edelgard, but of the four he probably has the worst odds. We'd get a popular, charming character with a full bow moveset, but Claude is also arguably the least important of the four to Three Houses's over all story structure.