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In this work, we develop a machine-learning-accelerated molecular dynamics (ML-MD) framework on the Cu\u2013Ag system to predict and control surface structure, identifying two competing descriptors: surface energy and adsorbate binding energy. We show that Ag\u2019s lower surface energy dominates in vacuum, forming a passive sheath, whereas a CO atmosphere reverses segregation and exposes active Cu sites through lateral phase separation. Decoupling the thermodynamic driving force from the kinetic diffusion barrier, we find that stability emerges not at near-equimolar ratios where segregation is strongest but rather at dilute compositions where weak driving forces and high kinetic barriers coincide. 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