We apply the ATPEW (Primordial Energy Wave) cosmological formulation to the Pantheon Type Ia supernova dataset, one of the most comprehensive compilations of standardized cosmic distance indicators. The objective is to evaluate whether large-scale cosmic expansion observations can be reproduced without invoking dark energy, within a framework where gravitational dynamics emerge from a structured primordial energy wave. Using the ATPEW distance–redshift relation, we reconstruct theoretical luminosity distance curves and compare them to Pantheon distance moduli across the full observed redshift range. The model preserves baryonic matter as the only material component while introducing scale-dependent structural energy effects that modify effective expansion dynamics. This analysis provides a direct quantitative comparison between ATPEW predictions and observational supernova data. Residuals and goodness-of-fit metrics are evaluated to determine the extent to which ATPEW can match the empirical expansion history. The results serve as a cosmological-scale falsifiability test of the model, extending previous ATPEW validations from Solar System dynamics, galactic rotation curves, and Milky Way structure to the largest observable scales. By confronting the theory with precision cosmological data, this work establishes whether ATPEW can offer a unified phenomenological description of gravity and cosmic dynamics without requiring a cosmological constant. This work is part of the ATPEW (Primordial Energy Wave) theoretical framework, a phenomenological approach to gravity and cosmic dynamics developed across multiple astrophysical scales.