Molecular cavity quantum electrodynamics (QED) systems, which contain strongly interacting molecules with quantized cavity photonic modes, are emerging quantum systems that exhibit new phenomena in chemistry and physics. Previous theoretical studies have shown that these hybrid light-matter states, so-called polaritons, , can modify chemical reactions via light-matter coupling. In addition, recent experiments have shown that molecular polaritons have drastically different transport properties compared to their bare excitonic components, paving the way for efficient and scalable optoelectronic devices based on polaritons . The light-matter hybridization also partially reduces the influence of phonons on the polariton, because the photon component does not couple to the phonon. This leads to the polaron decoupling effect and the well-known absorption lineshape narrowing. In particular, coupling N molecular exciton states with a quantized cavity mode produces two polariton states, commonly referred to as the upper polariton (UP) and lower polariton (LP) states, each containing light and matter excitation characters. There are N -1 remaining dark exciton states that do not mix with photonic states or have a significant transition dipole from the ground state, and are thus optically dark. Upon photoexcitation to UP, the system will quickly relax to the dark states and slowly transition to the lower polaritons. Polariton relaxation dynamics play a crucial role in understanding the polariton photoluminescence spectra, Electronic mail: depinghu@bnu.edu.cn b) Electronic mail: pengfei.huo@rochester.edu understanding the relative lifetime of the polariton and dark states, interpret the sub-average behavior of motional narrowing, and the transition rates between the polaritons and dark states, as well as the corresponding decoherence process. To study polariton relaxation dynamics, one often uses the Holstein-Tavis-Cummings (HTC) Hamiltonian to model the interplay between the exciton, photon, and phonon degrees of freedom (DOF). The HTC model couples many molecules, which are described as two-level systems, to both a cavity photon mode and phonon modes that are added phenomenologically to the molecules. In the strong-coupling regime, it has been shown that the HTC Hamiltonian captures the underlying physics of the cavity-QED systems , such as the polariton's relaxation dynamics and the polaron decoupling effect between excitons and their corresponding phonon modes .