The molecule-metal interface plays a critical role in chemical catalysis, offering rich opportunities for understanding and manipulating interfacial processes at the electronic scale. Of particular interest is the plasmon-driven reaction on plasmonic surfaces, where visible lights can be efficiently harnessed to drive chemical transformations. Quantum many-body framework provides a powerful tool box for unraveling the complex electronic structure of molecule-metal interfaces with high precision and predictive accuracy. This study combines Kohn-Sham (KS) density functional theory (DFT) and many-body perturbation theory (MBPT) to investigate the behavior of molecular charge carrier states at the metal surface. While KS DFT provides reliable ground state densities, it is less accurate in computing excited-state properties. To address this, we employ the GW approximation within the MBPT framework, which has demonstrated significant systematic improvements over DFT in predicting the excited-state properties of molecules and solids. To handle the quasi-particle (QP) energy calculation in a large-scale system of over thousands electrons, we utilize a newly developed stochastic GW package.This quantum many-body approach allows us to bridge atomic-scale factors with their influence on the electronic-scale energy changes. Focusing on the well-acknowledged molecular activation step of the important and realistic surface reaction, CO2 reduction (CO2RR), we study the vertical charged excitation - the key step in forming the transient ionic state. Specifically, in a CO2-Au prototypical system, we investigate how the molecular QP interacts with various adsorption sites on a plasmonic metal surface, revealing the importance of accurately accounting for the charging energy when determining chemical hot spots. We then explore the impact of subsurface oxygen, a specific atomic modification on the Cu surface, to showcase the interplay between substrate modification and adsorbate charging energy. Both studies demonstrate that state hybridization plays a critical role in determining excitation energy levels and molecular-surface coupling. Finally, an innovative approach to constructing Dyson orbitals by diagonalizing the perturbed Hamiltonian within the GW approximation is presented, aiming to capture the nuances of state hybridization. These studies collectively highlight the theoretical advancements in electronic structure calculations for realistic systems, made possible by the stochastic GW approach.