The achievement description is quite clear in what you need to do; but I can give some tips onto how to expedite this process.
1. Focus on engineers from rewards. The more engineers excavating the quicker it will go.
2. Think about build order. If you build every building in the game except defense matrix you should be left with 1-2 spaces left. This assumes you build at least 1 resistance comms and at least 1 power station.
3. Workshops and laboratories are optional; if you were super keen to get this done you could use gremlins from workshops to act as engineers; in reality your supplies would likely be better spent elsewhere.
You can optimise power usage by saving your second power station and a psi lab for the exposed power coils. The reason I suggest a psi lab is because it takes 5 power as apposed to some other early game facilities which cost less and so the gain would be less efficient.