Due to the inherent uncertainty in their deformability during motion, previous methods in deformable object manipulation, such as rope and cloth, often required hundreds of real-world demonstrations to train a manipulation policy for each object, which hinders their applications in our ever-changing world. To address this issue, we introduce GenDOM, a framework that allows the manipulation policy to handle different deformable objects with only a single real-world demonstration. To achieve this, we augment the policy by conditioning it on deformable object parameters and training it with a diverse range of simulated deformable objects so that the policy can adjust actions based on different object parameters. At the time of inference, given a new object, GenDOM can estimate the deformable object parameters with only a single real-world demonstration by minimizing the disparity between the grid density of point clouds of real-world demonstrations and simulations in a differentiable physics simulator. Empirical validations on both simulated and real-world object manipulation setups clearly show that our method can manipulate different objects with a single demonstration and significantly outperforms the baseline in both environments (a 62% improvement for in-domain ropes and a 15% improvement for out-of-distribution ropes in simulation, as well as a 26% improvement for ropes and a 50% improvement for cloths in the real world), demonstrating the effectiveness of our approach in one-shot deformable object manipulation.