We present TopoGaussian, a holistic, particle-based pipeline for inferring the interior structure of an opaque object from easily accessible photos and videos as input. Traditional mesh-based approaches require tedious and error-prone mesh filling and fixing process, while typically output rough boundary surface. Our pipeline combines Gaussian Splatting with a novel, versatile particle-based differentiable simulator that simultaneously accommodates constitutive model, actuator, and collision, without interference with mesh. Based on the gradients from this simulator, we provide flexible choice of topology representation for optimization, including particle, neural implicit surface, and quadratic surface. The resultant pipeline takes easily accessible photos and videos as input and outputs the topology that matches the physical characteristics of the input. We demonstrate the efficacy of our pipeline on a synthetic dataset and four real-world tasks with 3D-printed prototypes. Compared with existing mesh-based method, our pipeline is 5.26x faster on average with improved shape quality. These results highlight the potential of our pipeline in 3D vision, soft robotics, and manufacturing applications.