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