Nonlinear optical materials are widely used in optical and optoelectronic devices. The geometric, electronic, and NLO properties of copper-doped 2D silicon carbide nanoclusters (Cu@h-SiC) are investigated. The HOMO-LUMO gap (Eg) of the h-SiC nanocluster is significantly decreased by copper atom doping. All the isomers (A to G) showed a marked drop in Eg values. It is noticed that the Eg value decreased up to 46% of the original value. The partial as well as total density of state graphs for all seven structures indicate the emergence of new HOMOs between the frontier molecular orbitals of h-SiC. The isomer A exhibits a significant increase in both polarizability (α=669 au) and hyperpolarizability (βo=9.395×10-29 esu) values as compared to pure h-SiC. Global reactivity descriptors (IP, EA, and S) and low excitation energies endorse the enhanced NLO response of Cu@h-SiC. The EDDM (Electron density difference map) analysis is performed to gain insight into the electronic densities differences at the ground and excited levels. QTAIM analysis is used to investigate the type and nature of interaction between the Cu-atom and the h-SiC. TD-DFT calculations predict the absorption spectra in the visible and near-IR regions. This study may help in the fabrication of h-SiC-based materials with optimised NLO response.