Greenstone.Walker
Adventurer
How would you handle it the other way around? The characters are camped, all asleep except for one on watch. An attacker with a bow takes aim...How would you adjudicate the action and why?
What would your players say if you just said, "Character Juma is dead."?
Whatever ruling you make has to go both ways.
Me, I'd call for Initiative and use the Surprise rules.