This paper, Rethinking Cosmic Structure: A Transitional Sequel to Resolving the Hubble Tension Through Hypersphere Cosmology, develops a finite 3-sphere shell framework in which all matter resides on the outer shell while the interior 4-sphere core consists of dark energy. This transitional work provides the classical foundation for a forthcoming quantum extension. The model reframes standard cosmological observations—including CMB isotropy, baryon acoustic oscillations, gravitational lensing, and the Hubble tension—through geometric projection effects on a closed shell expanding at light speed. By comparing predictions against Planck CMB data, BAO surveys, and Type Ia supernovae (Pantheon+), the paper identifies clear observational tests that can validate or falsify the framework. This contribution is part of an ongoing series that extends from classical shell geometry into a broader quantum interpretation of cosmology.