Do you want deflection or permanent deformation. If you want to model permanent deformation this would be a non-linear analysis requiring Simulation Premium.
This is not a motion study. For FEA you would need flat contact surfaces (a little larger than the nodes, 4x+ for best result) and start with the surfaces already in contact.
linear will work as long as you dont expect a large deformation (causing a change in the direction of forces at any time) or any plastic deformation.
If you are wanting to model transient impact you would want to calculate the speed of the mushroom at the moment of impact. This again is a non-linear analysis.
I recently found a tutorial that agrees with what you said. I am trying to model permanent deformation so I have set up a non-linear dynamic simulation. The tutorial also stated that I needed to start with the surfaces already in contact so I have done that.
I am currently running the simulation as I type this so hopefully I set up the parameters appropriately.