As we started with a flat empty section of vacuum of space, would I be right in thinking that the curvature you have introduced is caused by the particles which subsequently respond to the curvature?
Yep you covered both options and we don't know which way it is. If we jump to your last question, we can add or even if it occurs at all.
If we regard the particles as resulting from the exchange of virtual gravitons, wouldn’t the gravitational “field” have to be in the flat empty section of vacuum of space first?
Correct and that is in line with QFT and the other fields. So here we have assumed a fully QM gravitational solution.
How do you square that with the idea that gravity is the curvature of spacetime caused by the presence of particles?
The extreme versions of quantum gravity and GR don't work together, they are competing descriptions of gravity. The quantum version mathematics returns the same answers as GR in the normal regions, they diverge widely in the macro and micro extremes without resolution on which is correct.
