I want to make a flatened cube take the shape of a face I am hoping to get some assistance in something I need for a project.

I am needing the cube here in the photos to actually take a fairly accurate impression of that face into the cube.

for my images attached,
I have created a cube that has been subdivided a bunch of times in EDIT MODE

I have simply moved the most center vertices with proportional editing enabled to make my 2nd image, but getting accurate face impression manually would take too much time and would like to know if there is a modifier that can be used then finally applied to make it stay like it?

Many Thanks
In front ortho view bake a displacement map of the face and apply it later to the subdivided plane. Later extrude the edges of the plane and make a face to close it.