For robot manipulation, both the controller and end-effector design are crucial. Soft grippers are generalizable by deforming to different geometries, but designing such a gripper and finding its grasp pose remains challenging. In this paper, we propose a co-design framework that generates an optimized soft gripper's block-wise stiffness distribution and its grasping pose, using a neural physics model trained in simulation. We derived a uniform-pressure tendon model for a flexure-based soft finger, then generated a diverse dataset by randomizing both gripper pose and design parameters. A neural network is trained to approximate this forward simulation, yielding a fast, differentiable surrogate. We embed that surrogate in an end-to-end optimization loop to optimize the ideal stiffness configuration and best grasp pose. Finally, we 3D-print the optimized grippers of various stiffness by changing the structural parameters. We demonstrate that our co-designed grippers significantly outperform baseline designs in both simulation and hardware experiments.