We introduce a new method for empirically determining the cosmic expansion history (H(z)) using galactic structure alone, based on a gravitational metric inflow framework that does not require dark matter halos. In this model, both spiral arm geometry and galaxy rotation curves arise naturally from the motion of spacetime itself, driven by a central gravitational mass and the Hubble parameter at the time of structure formation. We derive analytical expressions for the effective orbital velocity and pitch angle of the inflowing metric, demonstrating that these quantities encode the value of (H(z)) directly. By fitting observed rotation curves and spiral geometries from well-resolved galaxies, one can potentially extract empirical (H(z)) estimates and compare them to standard (Lambda)CDM predictions. Unlike traditional chronometers or BAO measurements, our approach relies solely on observed galaxy morphology and redshift, enabling a scalable and purely geometric reconstruction of the expansion history. We estimate that future surveys could yield (10^5) to (10^6) independent (H(z)) measurements using this method, offering a powerful new observational test of cosmology and gravity.