Adapting Large Language Models (LLMs) to specialized domains typically incurs high data and computational overhead. While prior efficiency efforts have largely treated data selection and parameter-efficient fine-tuning as isolated processes, our empirical analysis suggests they may be intrinsically coupled. We posit the Strong Map Hypothesis: a sparse subset of attention heads plays a dominant role in task-specific adaptation, acting as keys that unlock specific data patterns. Building on this observation, we propose From Parameters to Data (P2D), a unified framework that leverages these task-sensitive attention heads as a dual compass for both sample mining and structural pruning. To rigorously quantify the total pipeline cost, we introduce the Alignment Efficiency Ratio (AER) metric for both selection latency and training time. Mechanistically, P2D identifies critical heads via a lightweight proxy and uses them as a functional filter to curate high-affinity data, establishing a synergistic pipeline. Empirically, by updating merely 10% of attention heads on 10% of the data, P2D achieves an 8.3 pp performance gain over strong baselines and delivers a 7.0x end-to-end time speedup. These results validate that precise parameter-data synchronization eliminates redundancy, offering a new paradigm for efficient alignment.