Galactic-scale outflows driven by active galactic nuclei (AGNs) represent a commonly invoked feedback mechanism within galaxy evolution models. However, the interactions among interstellar gas on galactic scales, the propagation of AGN outflows, and the fundamental parameters of AGNs during their evolutionary processes remain poorly understood. Notably, powerful nuclear outflows are typically associated with the early stages of AGN activity, which are characterized by high accretion rates and weak narrow emission lines. In our analysis of a sample of quasars hosting Mg ii narrow absorption lines (NALs) obtained from the Sloan Digital Sky Survey, we identify a previously unobserved phenomenon wherein galaxy-scale inflow transitions to outflow dominance, concurrent with a notable increase in the strength of the narrow [O III] line, achieving a confidence level of 6.7σ. This indicates that while nuclear outflows diminish, galaxy-wide outflows intensify as AGNs evolve. These findings suggest that early-stage outflows interact with the interstellar medium on a galactic scale, thereby facilitating a gradual transition to galaxy-wide outflows. This provides observational support for the hypothetical multi-stage propagation of AGN outflows that globally regulates galaxy evolution.