Increasing concern about highly pathogenic avian influenza A (H5N1) is prompting the development of new antivirals directed toward conserved viral entities that are resistant to mutational escape. Here, at a multi-scale and precision-guided computational level, we employed a set of procedures to identify potential small-molecule inhibitors of the influenza virus PA endonuclease, a central component of the viral RNA polymerase complex responsible for cap-snatching of mRNA transcription. Through the structurally diverse drug-like dataset, we initiated structure-based virtual screens against the PA catalytic domain and received 1,500 high-affinity candidates. Top-scoring candidates were optimized using quantum mechanical density functional theory (DFT) computations and electron reactivity/orbital distribution analyses. Through re-docking of optimized geometries using DFT, lead molecules were subjected to exhaustive 1-microsecond molecular dynamics (MD) simulations and MM/GBSA binding free energy decomposition and principal component analysis (PCA) sampling of dynamic conformational topographies. Free energy surface mapping of low-energy basins and superimposition validation of pose stabilities verified sub-angstrom deviations. Significantly, 24782939 registered the least thermodynamic profile (ΔG = -45.8 kcal/mol), greatest H-bond persistence, and computed pIC50 of 8.17 using a machine-learned predictive model trained against structurally diverse chemical scaffolds. This multi-scale, integrated framework, involving atomic, energetic, and predictive scales, holds promise for translational applications of computational pipelines in antiviral discovery. Our findings nominate 24,782,939 as a highly promising inhibitor of PA endonuclease and have the potential to be developed into a next-gen therapeutic candidate against influenza A viruses.