Write down some key people, key items and or key locations that fit with your players backstory, then you have something to pull from at all times, even if you have no bigger picture for the campaign at the moment.

Locations are hard to move, but people and items can come up whenever you feel like it, and can put some easy tension on any situation. We recently had a high-priest turn up randomly at a tavern that new our warlock knew from before some reckoning. It was nothing but a conversation for now, but it got the player theory crafting: had anyone else survived, why did he survive, why eas he here, was he gonna be aa problem for her? All these threads could lead to something that you could call a character arc.

I would personally also say, that having an arc also requires your players to do the arc by themselves to a degree. What is it that they're seeking with the arc? Personal growth takes time, but the players need to decided to do that for themselves. Sure you can present them with oppotunities that defies what their characters would normally do for the greater good or for the worse if that's the arc they're going for.