Edit: A more intelligent way to do it is to remove the pin group during the simulation with the ***Vertex Weight Mix*** modifier.

You can create 2 groups: The *Pin* group (the whole paper except the 2 top corners) and a group with no vertex that you'll call *NoPin*. Give your paper a *Vertex Weight Mix* modifier, then *Cloth*, then *Subidivision Surface*. In the *Physics panel > Cloth > Shape* choose the pin group. In the *Vertex Weight Mix* modifier, select Vertex *Group A* (Pin) *and B* (NoPin). Choose *Vertex Set > VGroup A or B, Mix Mode > Replace*. Keyframe the *Global Influence* value the way you want in order to mix from A to B:

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

[![enter image description here][3]][3]

Previous answer:

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][2]][2]

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

[![enter image description here][4]][4]


  [1]: https://i.sstatic.net/fYZL2.jpg
  [2]: https://i.sstatic.net/pHgpB.gif
  [3]: https://i.sstatic.net/vp0x7.gif
  [4]: https://i.sstatic.net/86l3B.gif