This paper presents a novel Sensitivity-Guided Two-Stage Optimization (SGTSO) framework for magnetic gear (MG) design, introducing two fundamental methodological advances: (1) the adoption of global Sobol sensitivity analysis, which transcends conventional local sensitivity techniques by holistically quantifying both individual parameter effects and the interactions across the complete design space, and (2) the establishment of a mathematically guaranteed convergent two-stage optimization methodology that strategically decomposes high-dimensional problems into sequential subproblems. Unlike traditional one-factor-at-a-time sensitivity approaches that overlook parameter interdependencies, Sobol indices deliver quantitative evaluation of individual parameter contributions and coupling effects. The two-stage optimization architecture is rigorously proven to converge to near-optimal solutions under weak parameter coupling assumptions, with mathematically derived error bounds The optimized configuration achieves remarkable performance features: 65.4% suppression of inner rotor torque ripple, 27.2% reduction in outer rotor torque ripple, and 19.2% decrease in Permanent Magnet (PM) utilization, while preserving average torque output within a marginal 4.03% reduction. The proposed framework achieves a 5.25-fold enhancement in computational efficiency while maintaining mathematical convergence assurance, marking a substantial progression beyond conventional heuristic optimization paradigms.