The conjecture here is that a given volume of space must, at some point, randomly evolve into the quantum state you're interested. When the quantum fields align into the same state that a bunch of particles would represent, those particles appear out of the vacuum.
The trick that makes this work is that conservation laws don't apply on very small time scales. That's how virtual particles work after all. The energy can only be temporarily borrowed from the vacuum, unless you pay the energy cost to make that particle 'real' by destroying its virtual pair (see Hawking radiation).
You might imagine TV static, just random visual noise. There's no real reason the randomness can't line up to produce one single coherent frame before decohering. Just imagine that in 3 (or 11) dimensions.
I don't think an antiparticle pair is a strict requirement for virtual particles either. As long as energy is conserved on macro timescales, the universe doesn't really care what state the quantum fields are in.
Besides, even if you assume conservation of particle number, it only has to be eventual conservation. Suppose I borrow some energy from "over here" temporarily and accidentally assemble them into a perfect brain for a second, then they can disperse again, if they like.
A bigger question is, if energy were conserved globally, where exactly did those handy particles come from in the first place anyway?
Nucleated objects could be long-lasting, which blunts the Boltzmann brain (Bb) picture, as under fluctuation theory the Bb is ephemeral and time-reversible. On the other hand, it's historically been attractive to think of the nucleation of a inflating patch of spacetime (with low enough entropy that structure like galaxies might form as it expands and fragments gravitationally).