if causality exists, such that A causes B, does that not necessarily imply that A preceded B
Short answer: no. Causality loops are logically possible, although it’s not known whether our universe’s physics permit them. B could precede A and still be caused by it—and either A or B could be its own cause and its own effect.
and that time exists?
I think you would need to be clearer about what you meant by ‘time’ and ‘exist’. A conceptual model of potential relationships between states might be useful, and that could be what you mean by saying they are linked by time. As for existence, I’m not sure that time meets the criteria for us to be able to say it does or does not exist. What color is an electron? How salty are quadratics? The concepts do not apply.
Caledonian2 comments on Timeless Causality