Utilizing the explicit finite element method and the relative transmission loss coefficient (TLC) as the evaluation index, the vibration reduction performance of the square lattice sandwich plate with steel as the boundary and alternately filled with copper and silicone rubber was studied, and the impact of the square filling size on the structural vibration reduction performance was analyzed. Firstly, the finite element simulation model of the square lattice sandwich plate is established. Secondly, the relative transmission loss coefficient is introduced as the objective function, and the genetic algorithm is used to optimize the vibration reduction performance of the square lattice sandwich plate. For different application scenarios, the obtained optimization results show that the square lattice sandwich plate has tunability with different vibration reduction ranges. Finally, by analyzing the displacement field of the optimized topology at different frequencies, it can be seen that it is still under the action of the local resonance mechanism, showing strong attenuation of low-frequency elastic waves. This provides a new design idea for broadening the low-frequency vibration reduction performance and manufacturability of the sandwich plates.