Recent advances in structure-based protein design have accelerated de novo binder generation, yet interfaces on large domains or spanning multiple domains remain challenging due to high computational cost and declining success with increasing target size. We hypothesized that protein folding neural networks (PFNNs) operate in a ``local-first'' manner, prioritizing local interactions while displaying limited sensitivity to global foldability. Guided by this hypothesis, we propose an epitope-only strategy that retains only the discontinuous surface residues surrounding the binding site. Compared to intact-domain workflows, this approach improves in silico success rates by up to 80% and reduces the average time per successful design by up to forty-fold, enabling binder design against previously intractable targets such as ClpP and ALS3. Building on this foundation, we further developed a tailored pipeline that incorporates a Monte Carlo-based evolution step to overcome local minima and a position-specific biased inverse folding step to refine sequence patterns. Together, these advances not only establish a generalizable framework for efficient binder design against structurally large and otherwise inaccessible targets, but also support the broader ``local-first'' hypothesis as a guiding principle for PFNN-based design.