Maybe create a first simulation for the 2 corners (just pin the rest of the plane) and apply the simulation as shapekeys, keyframe the shapekeys:

[![enter image description here][1]][1]

Then create a second simulation and in the *Cache* make it start when it is supposed to:

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/pHgpB.gif
  [2]: https://i.sstatic.net/86l3B.gif