Ultrafast deposition of laser energy to a thin substrate-supported Au film enables formation of unique 3D surface morphologies, hollow nanobumps, possessing prospective linear optical properties useful for advanced plasmonic biosensors and nanoscale light sources. Here, we study the nonlinear optical response of such nanostructures by measuring second harmonic generation (SHG) from the individual nanobumps and their ordered arrays supporting local- and lattice-type plasmons at near-infrared frequencies. The results reveal the maximal SHG yield for the isolated nanobump correlated with its geometry-defined electromagnetic near-field enhancement at fundamental frequency. Additional (up to 110-fold) SHG enhancement with respect to the signal from a smooth Au film is achieved via a positive feedback provided through proper arrangement of the resonant nanobumps into the array supporting surface plasmon polariton resonant excitation near the fundamental frequency. Our results substantiate the laser-printed nanobumps as an inexpensive and flexible platform for nanoscale infrared-to-visible light conversion that can be applied for nonlinear plasmonics.