In a sense, causation actually is time. By that I mean that causes precede their consequences, and the causal sequence of events probably lies at the core of our everyday notion of the "flow of time" from past to future. I know that the literature speaks of time's "arrows", being different manifestations of time, but it seems to me they all reduce down to causality. As always, when speaking with you, I'm prepared to be corrected.
I can think of a counterexample. Suppose I have two events that have "spacelike" separation, meaning that they occur far enough away from each other that a light ray can't travel from the first event in time to arrive before the second event. By construction, one event cannot be said to cause the other. In fact, the time ordering of the events is observer-dependent: in one inertial frame event "1" might happen before event "A", while in another event "A" occurs first. But in every frame, they do have a well-defined ordering in time, despite the lack of causality.