Exploring the design and control strategies of soft robots through simulation is highly attractive due to its cost-effectiveness. Although many existing models (e.g., finite element analysis) are effective for simulating soft robotic dynamics, there remains a need for a general and efficient numerical simulation approach in the soft robotics community. In this paper, we develop a discrete differential geometry-based numerical framework to achieve the model-based inverse design of a novel snap-actuated jumping robot. It is found that the dynamic process of a snapping beam can be either symmetric or asymmetric, such that the trajectory of the jumping robot can be tunable (e.g., horizontal or vertical). By employing this novel mechanism of the bistable beam as the robotic actuator, we next propose a physics-data hybrid inverse design strategy for the snap-jump robot with a broad spectrum of jumping capabilities. We first use the physical engine to study the influences of the robot's design parameters on the jumping capabilities, then generate extensive simulation data to formulate a data-driven inverse design solution. The inverse design solution can rapidly explore the combination of design parameters for achieving a target jump, which provides valuable guidance for the fabrication and control of the jumping robot. The proposed methodology paves the way for exploring the design and control insights of soft robots with the help of simulations.