The 3D appearance after you took the photo off is a guess we made based on knowledge. Our ability to stay alive in critical situations is based on the ability to make such guesses.
If we did never see the photo we would have much less knowledge available, but I'm sure many of us would still see the approximate depth due having some cumulated data collected by watching 3D meshes. I guess some people who never have used 3D software could also make the right guess.
If the mesh was perfectly drawn of polygons which in 3D were uniformly sized, the size was known and the imaging was known (=known camera properties) the image would be parseable back to 3D because we could calculate the orientations and placements of the original 3D polygons.
Of course only those areas could be parsed which have totally visible polygons. And the imaging must have strong enough perspective. A parallel projection or so nearly parallel projection that the image resolution cannot show differences would fade all depth.
I do not know if someone has ever programmed a working system for the full job, but descriptive geometry textbooks have surely about 100 years contained how to interpret photos in 3D when there's enough known forms and measures.
In this site I have written some answers to questions where 3D images were wanted to be reconstructed from a 2D perspective images. The forms of the objects were known (rectangles, cubes), they needed only right placements and position angles.
Your manually drawn mesh is more complex than by computer made 3D polygon meshes. You have tried to guess the surface forms and your curves are drawn along those guesses. The mesh is NOT made of planar polygons and their sizes in 3D vary. The problem is a light year tougher than the case of regular planar polygons.
An Artificial intelligence program perhaps could be taught to understand your way to draw assuming you did have some consistently used rule and knowledge of the right 3D form. But I must skip that subject due the lack of knowledge. The case is hopeless if you drew it by changing your estimation rule randomly.
The original photographed surface has some degree of continuity when smoothed to image resolution scale. The depth and the surface orientation do not jump fully randomly between adjacent pixels. Also the the number of possible surfaces behind your mesh decrease radically if that assumption of continuity is used. Another as useful assumption (not a truth if you didn't make it true) is to think that in 3D the lines were the shortest paths along the surface between the points or at least locally minimum length paths.
As said, I do not know enough, mathematicians are needed to reveal some actual details.