Yup,cloth simulation ,  have the face horizontal looking up , and drop the hi-res prop square onto it in a cloth simulation , you only need maybe 15 frames . Use one of the earlier frames where the cloth is only partially draped.

Or select a row of points around the cloth edge to be allocated to coreogaphed group. And set keyframes at 0 with the cloth just over the face , not touching , and then at say frame 20 with it part way down the head.  Set keyframe , and run the cloth simulation . Using choreographed will stop the cloth edge from dropping .

In either case you may need a light cloth to get the tight conforming thats in the picture.