Unmanned sailboats rely on wind and solar energy for long-duration marine missions, yet their navigation performance is strongly constrained by sail aerodynamics, hull hydrodynamics, and time-varying wind fields. Due to their underactuated nature and the critical influence of sailing speed on safety and efficiency, this paper addresses the time-optimal global path planning problem for unmanned sailboats in complex marine environments. A customized velocity prediction program (VPP) is developed to accurately estimate sailing speeds under different true wind angles, explicitly accounting for the drift angle effect. A time-efficient cost function is constructed and integrated into the Rapidly exploring Random Tree Star (RRT*) algorithm. To improve computational efficiency, three strategies, including goal-biased sampling, artificial potential field guidance, and adjacent domain expansion, are introduced. The proposed hybrid algorithm imposes no restrictions on path step size or direction, ensuring asymptotic optimality while complying with sailboat dynamic constraints. Comparative simulations and validation tests using multiple VPP datasets demonstrate that the method is feasible, efficient, and widely applicable for unmanned sailboat navigation.