[InclinedPlane]

Ablation is the best bet if you need to move something as much as possible as fast as possible. And for that you want a device which outputs a lot of EM radiation at tremendous power levels and ideally is as compact as possible in order to transport it near enough to the object. Nuclear weapons meet all those criteria and so are likely to be the best tools for pushing around big rocks quickly on short notice. You simply explode them at an appropriate stand-off distance and the energy release of mostly soft x-rays causes the surface near the explosion to ablate, generating thrust.