The assassin ability doesn't say it has to be at the start of combat, but the surprise rules do.Actually, it goes on to say, "In addition, any hit you score against a creature that is surprised is a critical hit."
So it doesn't have to be a creature at the beginning of combat. They just have to be surprised.
"Any character or monster that doesn’t notice a threat is surprised at the start of the encounter. If you’re surprised, you can’t move or take an action on your first turn of the combat, and you can’t take a reaction until that turn ends."