We study the formation of planar network nanostructures, which develop during metal deposition on initially smooth surfaces of layered compounds. Using in situ low-energy electron microscopy for dynamic observation and high-resolution transmission electron microscopy for structure analysis, we have observed the rapid formation of hexagonal networks of linear "nanofolds" with prismatic cavities on top of layered VSe2 crystals. Their formation results from relaxation of compressive strains which build up during Cu intercalation into a thin surface layer.