Using e + e − collision data at 13 center-of-mass energies ranging from 4.600 to 4.951 GeV collected with the BESIII detector, we conduct the first search for the e + e − → $ {K}_S^0{K}_S^0{h}_c $ process and investigate the resonance structures in the cross section line shape. No significant signal is observed, and the upper limits of the Born cross sections at each center-of-mass energy are presented. The ratio $ \frac{\sigma \left({e}^{+}{e}^{-}\to {K}_S^0{K}_S^0{h}_c\right)}{\sigma \left({e}^{+}{e}^{-}\to {K}_S^0{K}_S^0J/\psi \right)} $ is determined to be 0.15 ± 0.22. This result indicates that if vector states exist in this energy region, their decay into h c is significantly suppressed compared to decays into J / ψ .