We present a framework for efficiently preparing meson wave packets for a lattice gauge theory on quantum devices. The method is demonstrated using a (1+1)D Z2 lattice gauge theory coupled to Kogut-Susskind staggered fermions as a testbed. Our approach systematically constructs mesonic excitations on top of the ground state with well-defined momentum. Using a quantum subspace expansion approach with a symmetry-preserving basis, we obtain explicit operators for creating such excitations, which in turn allow us to construct localized wave packets. By simulating the scattering process of two meson wave packets with Tensor Network States, we identify both elastic and inelastic scattering processes during the dynamics. In addition, we also provide a resource-efficient decomposition for the operators creating mesonic wave packets into elementary quantum gates, thus enabling quantum simulation of meson scattering in the (1+1)D Z2 lattice gauge theory.