Second-order nonlinear metasurfaces have proven their ability to efficiently convert the frequency of incident signals over subwavelength thickness. However, the availability of second-order nonlinear materials for such metasurfaces has so far been limited to III-V semiconductors, which have low transparency in the visible and impose constraints on the excitation geometries due to the lack of diagonal second-order susceptibility components. Here we propose a new design concept for second-order nonlinear metasurfaces on a monolithic substrate, which is not limited by the availability of thin crystalline films and can be applied to any non-centrosymmetric material. We exemplify this concept in a monolithic Lithium Niobate metasurface with cylinder-shaped corrugations for enhanced field confinement. By optimizing the geometrical parameters, we show enhanced second harmonic generation from a near-infrared pump beam with conversion efficiency above 10-5 using 1 GW/cm2 pump intensity. Our approach enables new opportunities for practical designs of generic metasurfaces for nonlinear and quantum light sources.