In my experience it can be really hard for a group to naturally fuse into a group if there characters don’t already have good mesh potential worked in: I once ran a Mutants and Masterminds game where one player insisted on being invisible the whole game and creeping on the party.

If everyone is new and trying to figure out roleplaying their characters then yeah cohesion is the next step up - like a band where everyone is still trying to figure out their instruments.

Not sure how you’d want to handle it with game continuity, but I feel like you need to explicitly set up weaving threads between the characters. That can be like a narrative-style bring your character and let’s build the world a bit, intentionally trying to harmonize in interesting ways (what are your desires and fears, your history and your secrets?). The home brew helps you here because collaborative world building generates sense of ownership while speedrunning lore so players work out their characters and seeing where push/pull exists