Suppose an AGI comes into being. (I mentioned Boltzmann brains as a sort of lower bound on what it would take for this to occur: the universe being very large, this is virtually guaranteed to happen at least once at some point somewhere.)
What happens to the newborn godling? This greatly depends on its immediate environment. If it's born into a region of spacetime where it's surrounded by dumb matter (any sub-foom intelligence being effectively "dumb" for these purposes), then it quickly takes over its future light cone.
If the space it controls gets large enough (which it will, given time), then it will have to contend with the possibility of contenders emerging, Boltzmann gods like itself spontaneously forming out of the ether (or rather, since it's eaten its future light cone, out of the computronium). Luckily for it, it has a vast resource and positional advantage over the upstarts, by virtue of having time and space to prepare. The upstarts have minds that can fit into a volume small enough to form by pure chance (and the Law of Large Numbers), whereas the standing god has no such limitations.
So we can anticipate that, in a conflict between two Boltzmann gods, the firstborn would win.
If we further postulate that full-strength time travel is possible, then it follows that a Boltzmann (or other) god would eventually figure this out and travel back to the beginning of the universe, so as to control all of everything. By the previous argument, an AGI with first-mover advantage from the beginning of the universe would be able to easily prevent any serious threats to itself from arising. Thus, only one godling will ever rise to full strength, only one will go back in time and set itself up, and there will be no (successful) revolutions.
From this we may infer that either: (1) the universe is not that big; (2) fully general time travel isn't possible; (3) we are instrumental to the Robot God's plans in some way; (4) we are a component of the RG's mind; (5) we are a side effect of the RG's computation and it doesn't notice or care enough to kill us.
I don't really think 1, 3, or 4 is really plausible. 5 without 2, in such a way that 2 is still false of the sub-reality that the side effect created, would probably recurse until we got a non-time-traveling side-effect sub-reality. That leaves 2: you can't travel back in time to before the invention of the time machine (or some other such restriction).
Ah ok. So it seems we have different conceptions about how and when Boltzmann brains arise. As I understand it, the vast majority of Boltzmann brains will arise after what we would normally call the heat death of the universe. They won't in general have the resources to control their future light-cone because it won't have enough usable energy. That's aside from the fact, that this assumes Boltzmann brains that have their beliefs about reality around them in some way correlated with reality, something which does not necessarily have such a high probability (this is the the classic argument behind why you might be a Boltzmann brain who has lasted a fraction of a second and will soon dissolve back into chaos.)
If someone gets cremated or buried long enough for eir brain to fully decompose into dirt, it becomes extremely difficult to revive em. Nothing short of a vastly superhuman intelligence would have a chance of doing it. I suspect that it would be possible for a superintelligence to do it, but unless there's a more efficient way to do it, it would require recomputing the Earth's history from the time the AGI is activated back to the death of the last person it intends to save. Not only does this require immense computational resources that could be used to the benefit of people who are still alive, it also requires simulating people experiencing pain (backwards). On the other hand, this saves people's lives. Does anyone have any compelling arguments on why an FAI would or would not recreate me if I die, decompose, and then the singularity occurs a long time after my death?
Why do I want to know? Well, aside from the question being interesting in its own right, it is an important factor in deciding whether or not cryonics is worth-while.