Our FNDMC results closely match the experimental data (within 0.1 eV) as well as the previous study for the top site with -0.57 (5) eV. Additionally, our results exhibit minimal variation between other adsorption sites and show distinct energy gaps of 0.34 eV to 0.39 eV between the top site and the rest, consistent with experimental observations that CO favors the top site at low coverages. This alignment with experimental data confirms the reliability of our improved FNDMC workflow. These findings further underscore the limitations of DFT methods in accurately predicting adsorption site preferences and highlight the superior performance of FNDMC in resolving the CO adsorption puzzle on copper surfaces.