2D materials are promising candidates as nonlinear optical components for on-chip devices due to their ultrathin structure. In general, their nonlinear optical responses are inherently weak due to the short interaction thickness with light. Recently, there has been great interest in using quasi-bound states in the continuum (q-BICs) of dielectric metasurfaces, which are able to achieve remarkable optical near-field enhancement for elevating the second harmonic generation (SHG) emission from 2D materials. However, most studies focus on the design of combining bulk dielectric metasurfaces with unpatterned 2D materials, which suffer considerable radiation loss and limit near-field enhancement by high-quality q-BIC resonances. Here, we investigate the dielectric metasurface evolution from bulk silicon to monolayer molybdenum disulfide (MoS2), and discover the critical role of meta-atom thickness design on enhancing near-field effects of two q-BIC modes. We further introduce the strong-coupling of the two q-BIC modes by oblique incidence manipulation, and enhance the localized optical field on monolayer MoS2 dramatically. In the ultraviolet and visible regions, the MoS2 SHG enhancement factor of our design is 105 times higher than that of conventional bulk metasurfaces, leading to an extremely high nonlinear conversion efficiency of 5.8%. Our research will provide an important theoretical guide for the design of high-performance nonlinear devices based on 2D materials.