Causality is a concept that exists within a universe, because it's bound to time, which also a concept that exists within a universe. The physical law of causality (which can be expressed as both "events of the present are fully defined by system states at previous times" and the time-reversed equivalent, that the past states are fully defined by the future) are only coherent concepts within the framework of specific physical laws that govern this universe. Not every set of possible physical laws gives rise to causality, or even time.
In Conway's Game of Life, the future state of the board is also fully determined by the past, although there is no time reversal symmetry.
Judea Pearl's causality is similarly bound to applying within the context of a timeline and universal law.
Again in Conway's Game of Life, you can implement Turing machines and run simulations of any scenario. Hypothetically you could have artificial life in such a simulation, which might conduct experiments to learn the physical laws of the cellular automaton that governs their world.
But those laws, their perception of cause and effect, only exist within the context of that simulation, and within their simulated timeline. Their "time" is a state variable of the simulation.
No experiment conducted by creatures within the Game of Life could determine why their simulation is running in the first place, or why its initial conditions were chosen the way they were. The computer running their simulation is outside the laws of their universe. To ask "what was the value of Conway.simTimeIndex before the Game was started?" doesn't make sense. The laws that govern the commencement of Games cannot be perceived from inside the Game.
On our own level, the notion of cause and effect is a concept that is coherent within our universe and its concept of time. To ask whether our universe had a cause, or was preceded by something, doesn't make sense. It might or it might not have; that depends on the laws that govern the commencement of Universes, which we cannot measure from observations inside of our universe. If there is any law of meta-causality or time, on the level of reality at which universes are created, we will not identify it via measurements conducted within this universe.