Low Earth Orbit (LEO) satellite systems serve as critical infrastructure for internet of things (IoT), military, and emergency missions due to their low-latency global coverage. This work leverages time-hopping (TH) technology’s interference resilience and low-probability-of-intercept characteristics through a TH communication architecture where signals are distributed across pseudo-random TH sequences. The receiver implements joint de-hopping and carrier offset synchronization to enable multi-hop coherent combining for signal-to-noise ratio (SNR) enhancement in low- \(E_\textrm{b}/N_\textrm{0}\) regimes. To overcome TH pattern randomness and dynamic frequency-phase distortions, we develop a genetic algorithm (GA)-driven hierarchical estimation framework comprising coarse and fine synchronization stages. Application-specific genotype encoding and dedicated crossover mechanisms, guided by a signal-energy fitness metric, ensure rapid convergence to global optima. Numerical simulations demonstrate that the proposed architecture achieves near-theoretical bit error rate (BER) performance with \(5.61 \times 10^{-5}\) symbol-rate-normalized frequency root mean square error (RMSE) and 0.044 rad phase RMSE at 4 dB per-hop \(E_\textrm{b}/N_\textrm{0}\) , outperforming conventional single-stage estimation strategies in precision and robustness.