Single atoms, and in particular the least reactive noble gases, are difficult to immobilize at room temperature. Ion implantation into a crystal lattice has this capability, but the randomness of the involved processes does not permit much control over their distribution within the solid. Here we demonstrate that the boron nitride nanomesh, a corrugated single layer of hexagonal boron nitride (h-BN) with a 3.2 nm honeycomb superstructure formed on a Rh(111) surface, can trap individual argon atoms at distinct subsurface sites at room temperature. A kinetic energy window for implantation is identified where the argon ions can penetrate the h-BN layer but not enter the Rh lattice. Scanning tunneling microscopy and photoemission data show the presence of argon atoms at two distinct sites within the nanomesh unit cell, confirmed also by density functional theory calculations. The single atom implants are stable in air. Annealing of implanted structures to 900 K induces the formation of highly regular holes of 2 nm diameter in the h-BN layer with adjacent flakes of the same size found on top of the layer. We explain this "can-opener" effect by the presence of a vacancy defect, generated during the penetration of the Ar ion through the h-BN lattice, and propagating along the rim of a nanomesh pore where the h-BN lattice is highly bent. The reported effects are also observed in graphene on ruthenium and for neon atoms.