I know Larian makes "classless" systems in their other games. D&D doens't work like that, and many Origin characters have classes tied to their backstory. How would Wyll the Rogue work, or Shadowheart the Wizard?
If Larian wants to allow the origins to switch classes, I think that fixing the first level of each origin class as the default, and waiving the requirements for multi-classing would be the way to go. So every Origin would always have 1 level in their default class which can't be changed or removed, but you could change up their future levels.
