On the level of higher dimensions, it's difficult for us to perceive how cause -> effect would play out, but it's similar to how you would influence a drawing of a 2D stick figure. You could draw a house next to the stick figure, and that would cause the house to exist, but to the stick figure it would only perceive a single line with a start and finish on 1 dimension.
To that stick figure, cause and effect would be perceived as the two points on the line, though your four dimensional pencil caused it to exist on a different dimensional level.
• You can have causality in space rather than time: e.g. a convolutional image filter at pixel 13 might consider pixels 12, 13, 14 (of which the first two are causal and the last is non-causal, if we consider higher numbers as going "forward")
• You can have non-causal filters in time: e.g. audio compression at time 0:30 might consider not only the portion of audio from 0:00 to 0:30, but also the audio from 0:30 to 2:33. (This doesn't seem that remarkable, because the track has already been recorded, so it's not in "real time".)
• Finally, what we usually think of as intuitive causality in "real time" is simply a question of entropy. We think of a person dying because she was shot by a bullet, but we could also replay the movie backwards and think of all the tissues of a human body coming together in such a way as to propel the bullet backwards at a high velocity - in other words the wound causes the bullet to fly! The only reason we don't think of it this way is because the latter explanation decreases rather than increases entropy. As it turns out, physicists can show that entropy is also the exact reason why we remember the past and not the future. (And if we did remember the future and not the past, we would simply think of the future as the past and vice versa, so things wouldn't feel any different.)
This is not a god argument, there might be natural processes that can trigger such events.
We really don't. We don't have any physical evidence of anything from before the big bang (presuming that's what we call the "beginning"). Zero. All we have is people having views on the current situation, trying to apply those views backwards to "before", where they may or may not fit, and saying "I think it's like this".
You could - hypothetically - pause the computer, check its state, change a few variables, and the simulation would experience instant modifications.
A slow simulator could take many "real" time units to calculate each in-simulation time frame - and this would be invisible in-simulation.
And so on.
You have a fully causal system, but the simulation is ruled by its own independent emulation of causality.
Of course a computer implies a conscious user. But let's attempt some wild speculation and suggest that a "simulation" could also be a completely natural process - something that happens in a much bigger causal substrate: a kind of causal symmetry breaking, where a subset of possible relationships crystallises out of a bigger set of possibilities and then continues independently, losing some degrees of freedom.
A simple two level topology is the simplest possible model. But "causality physics" could allow all kinds of topologies - nested, circular, fractal, etc.
I don't think that's "by definition". That's by observation of an example of one.