The computer, and the external universe of which it is unaware, still have time.

Total amateur here: how do we know that time did not exist before the beginning of the universe?

Almost-total amateur here: We don't.

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".

I don't think this is an accurate analogy. The computer's space-time and your space-time are the same in this analogy. The space-time that our universe exists in would not be the same as the space-time that some extra-universe process would be inside if the big bang theory is accurate. This isn't an analogy for causality without time, this is causality for the creation of our universe if the big bang theory is wrong and space-time didn't expand out of a point some billions of years ago, ie. that our space-time existed "before" the big bang and there were processes outside of our universe that were still inside of the same space-time as ours.

If the computer is simulating a spacetime, they're not the same.

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.

Good point which brings us to a simple explanation. Time zero isn't when the h/w is booted, it's when the software is started. As unpopular as the simulation theory is, many difficult issues can easily be thought about. Except for the rest of the turtles.

Although it raises an interesting question, because physics has a lot of issues with time. Just as in the computer example, why could we not imagine that our universe exists inside the space and time of larger superuniverse, and perhaps the phenomena that explain times arrow is easily observable in that universe, but not in ours.