Silicon carbide (SiC) MOSFETs, as leading wide bandgap semiconductor devices, exhibit superior stability and reliability under high-temperature, high-switching frequencies, and high-power density operational conditions. SiC MOSFET with fan-out panel-level packaging (FOPLP) utilizes a redistribution layer (RDL) to substitute bonding wires, achieving low thermal resistance, electrical resistance, and parasitic inductance. This study proposes an optimal design strategy for SiC MOSFET FOPLP, considering parasitic inductance suppression, heat dissipation, thermal-mechanical reliability, and insulation enhancements. First, we establish the parasitic inductance, heat transfer network, and thermomechanical stress physical analytical models of SiC MOSFET FOPLP. Subsequently, the non-dominated sorting genetic algorithm (NSGA-II) and the improved multi-objective particle swarm optimization algorithm (MOPSO) are integrated to realize the co-optimization of parasitic inductance, thermal resistance, thermal stress, and electric field intensity distribution. Finally, we attain the optimal parameters of the SiC MOSFET FOPLP, i.e. chip thickness (x₁), solder thickness (x₂), RDL thickness (x₃), and chip side length (x₄) as 0.25 mm, 0.05 mm, 0.35 mm, and 6.00 mm, respectively. Additionally, according to comparison the MOPSO algorithm exhibits faster convergence and superior diversity than NAGA-II in the electrical-thermal-mechanical multiphysics co-optimization. Generally, the proposed physical analytical models combined with a multi-objective optimization method have a substantial guidance and forward-looking prospect on the design of SiC MOSFET FOPLP.