If the universe is static, then there is no "repeatably observable causality" or indeed any causality at all. In that scenario any perception of time and causality would inherently have to just be our perception lying to us about a past that we have had not part in, if it exist in any sense at all. If so, we have not had this conversation, and your experience of it is just a static momentary perception of having had it.
Maybe time is a spatial dimension, and there are infinite moments of consciousness fixed in the same spatial location with no time passing.
Consider how you'd tell if a drawing is an individual drawing or a frame from a cartoon if all you have to go by is that single frame. You can argue that the drawing hints convincingly at motion, but that does not require that this motion has taken place.
Or consider a trace of a simulation, sliced and diced into snapshots of individual moments. We can argue that it's unlikely any entities in such snapshots would have consciousness, but if we're arguing on the basis that we appear to experience the motion of time, we'd equally make that argument if we were wrong about consciousness and indeed locked in snapshots of individual moments. We can even construct simulations where individual parts look causally connected but where the existence of one calculated frame tells us nothing about whether any individual other frames have even ever been instantiated (e.g. imagine a very complex function over time, where only punctuated values have ever been calculated).
I'm not saying I believe that is our situation - I'm saying we can't distinguish between that and an infinite set of other possible options, because "from the inside" there is an infinite set of possibilities that could all look the same from our vantage point. We can debate which possibilities seem more likely, but they will always be speculation as long as we're locked inside the asylum, so to speak...
Incidentally, this is an argument for a materialistic view of the universe, not against it, on the basis that absent a way of "peeking out" and seeing our situation from the outside, it's meaningless to treat the world as anything but what we measure and perceive - it doesn't matter whether or not this world is what it seems like to us or not as long as it is the only view we have of it. We just can't say if it is some inherently true objective view of the universe, and most likely it won't make any difference to us.
It only makes a difference when we tinker with philosophy around the edges, like these conversations about whether what we experience can tell us anything about the experience of other entities.