Abstract: Quantum metrology establishes fundamental precision limits for parameter estimation, yet standard Quantum Cram & eacute;r-Rao Bound (QCRB) becomes insufficient in the finite-data regime. In this article, the QCRB is systematically tighten using a hybrid classical-quantum framework by incorporating generalized unbiasedness constraints through test observables. These frequentist bounds form a hierarchy converging asymptotically to the QCRB as more measurements are performed. These hierarchical frequentist bounds are validated for single-qubit phase estimation on a photonic platform.