Traumatic brain injury (TBI) triggered by transient impact loading is a major challenge for protection design and rapid post-exposure assessment, in part because actionable tissue-level metrics are rarely available within operational time constraints. High-fidelity finite element (FE) head models can resolve heterogeneous, time-dependent brain deformation and provide strain-based injury indicators, but their computational cost prevents low-latency screening and large-scale parametric studies. Meanwhile, studies that couple biomechanics to imaging or histology increasingly indicate that early-time deformation patterns are associated with injury-relevant neuropathology, motivating fast predictors that retain physical interpretability. We develop a neural-network surrogate that predicts injury-relevant brain responses directly from an input loading waveform. Training data are generated primarily from high-fidelity FE simulations spanning a representative range of waveform shapes, directions, and boundary conditions. The surrogate targets the maximum principal strain (MPS) field in brain tissue, together with derived scalar summaries. Methodologically, waveform-to-field prediction is posed as a function-to-field operator approximation: a waveform encoder learns a compact representation of the loading history, and a coordinate-conditioned decoder reconstructs MPS at standardized brain locations. Across held-out impact scenarios, the surrogate reproduces FE-predicted MPS patterns and peaks with strong agreement while reducing evaluation time by orders of magnitude, enabling near real-time estimation once a waveform is available. This complements prior demonstrations of fast whole-brain strain inference trained against FE ground truth and emerging near real-time predictors driven by measured head-motion inputs. The proposed framework supports (i) injury-aware protective-system development via rapid exploration, uncertainty analysis, and optimization, and (ii) field- or clinic-facing decision tools that convert measured impact waveforms into immediate, interpretable strain-based risk screening.