This paper presents a novel framework that combines model-based and learning-based approaches to solve the problem of non-prehensile manipulation. Combining the efficiency of model-based approaches with the robustness of learning-based approaches, we achieve sample-efficient learning by designing a demonstration-guided deep reinforcement learning (RL) based on computationally efficient contact implicit trajectory optimization (CITO) that explicitly considers contact points. Furthermore, we present a simulation-to-real transfer approach using a privileged training strategy to enable a robot to perform pivot manipulation using only proprioception, vision, and force sensing, without privileged information (e.g., object mass, size, or pose). Evaluation on multiple pivot tasks demonstrates the successful implementation of the simulation-to-real transfer. Further details can be found in the video provided at the YouTube link.