The propensity of trace amounts of sulfur adsorbed on coinage metal(111) surfaces to dramatically enhance surface dynamics has been demonstrated by STM observations of accelerated 2D island decay for Cu and Ag. It is generally accepted that this enhancement is due to the formation of adsorbed metal-sulfur complexes, which facilitate surface mass transport of the metal. These complexes were originally proposed to form on terraces following the extraction of metal atoms from step edges and subsequent combination with sulfur on the terraces. However, even when thermodynamically feasible, this mechanism may not be kinetically viable for some complexes due to limited coupling of the complex concentration to the surface diffusion flux of metal atoms. Focusing on the case of Cu, we assess various scenarios where complexes are formed either on terraces or instead directly at step edges, the latter being a new paradigm. A new pathway is proposed for the formation on terraces. A rich variety of structures incorporating S at step edges exist, which could provide a viable source for complexes, at least from a thermodynamic perspective. However, it is necessary to also assess the activation barrier for complex formation and detachment from step edges. This is facilitated by the nudged-elastic-band analysis of the minimum energy path for this process utilizing machine-learning derived potentials based on density functional theory energetics for the metal-sulfur system.