I'm it work now, so I can't verify, but I have a scene where a piece of cloth needed to be blown away, revealing an object.
To control this, I used a dummy attached to the cloth and then I "projected" the dummy, which picked up the cloth. I'm just starting to experiment with this stuff so there may be a better way.
Another option to consider is that you can change the physics state of an object in the time line which may allow you to control when the simulation starts.
Again, this is just from memory; I'll have to check tonight.