Reconstructing full atrial activation maps from the sparse coverage of clinical electroanatomical mapping is an ill-posed inverse problem. Standard approaches interpolate extracted local activation times (LATs), discarding raw waveform information and producing maps that can violate wavefront physics in unsampled regions. We extend the Eikonal–Poisson parameterization to the volumetric intracardiac setting, recovering the full left-atrial activation map by directly fitting raw unipolar EGM waveforms. The activation map is parameterized through a volumetric propagation-direction field: for each candidate field, a single linear Poisson solve recovers an eikonal-consistent activation-time map, keeping the pipeline fully differentiable. The objective combines normalized EGM waveform error with a LAT-anchored regularization term penalizing deviations from the steepest negative deflection at each measurement location. An ensemble of five independently initialized instances is optimized per configuration using ADAM in JAX. We evaluated the method on a patient-specific LA geometry with monodomain-simulated EGMs (sinus rhythm, Bachmann's bundle onset), varying measurement count from 10 to 711 with repeated random subsets. RMSE dropped from 7.5–22 ms at Np = 10 to 2.5–5 ms at Np = 100, with endocardial and epicardial errors tracking within 0.2 ms throughout. At Np = 50, the Bachmann's bundle region remained identifiable; at Np = 200, it was clearly delineated alongside atrial floor activation. The Eikonal–Poisson constraint enforces wavefront consistency across the full atrial volume by construction, including unsampled regions — a guarantee data-only interpolation cannot provide. This advantage is expected to be most significant in pathological substrates with conduction heterogeneities, representing the primary direction for future work.