Buckling of membrane-substrate systems provides an effective route for generating complex surface morphologies. However, a systematic inverse-design approach for 3D buckling morphologies has yet to be established, particularly when nonlinear path dependence is involved. In this work, an optimization framework based on density-based topology optimization is developed to realize prescribed complex surface patterns and to achieve full control of post-buckling behavior through two distinct capabilities: programming pattern evolution along prescribed biaxial loading paths, and eliminating path dependence to obtain identical target patterns under different loading paths. The framework incorporates hyperelasticity together with an energy interpolation strategy to stabilize low-density regions in large-deformation nonlinear simulations. A fixed-compression value is used to reach the post-buckling regime, with both simultaneous and sequential equi-biaxial compression paths considered to capture path-dependent effects. The proposed framework demonstrates full control of complex 3D buckling morphologies: prescribed surface patterns are achieved under both simultaneous and sequential loading. Distinct surface patterns can be programmed to emerge sequentially along prescribed loading paths, enabling controlled pattern evolution during deformation. It is further demonstrated that identical target patterns are obtained under different loading paths, effectively eliminating path dependence in the final post-buckling morphology.