Classical policy search algorithms for robotics typically require performing extensive explorations, which are time-consuming and expensive to implement with real physical platforms. To facilitate the efficient learning of robot manipulation skills, in this work, we propose a new approach comprised of three modules: (1) learning of general prior knowledge with random explorations in simulation, including state representations, dynamic models, and the constrained action space of the task; (2) extraction of a state alignment-based reward function from a single demonstration video; (3) real-time optimization of the imitation policy under systematic safety constraints with sampling-based model predictive control. This solution results in an efficient one-shot imitation-from-video strategy that simplifies the learning and execution of robot skills in real applications. Specifically, we learn priors in a scene of a task family and then deploy the policy in a novel scene immediately following a single demonstration, preventing time-consuming and risky explorations in the environment. As we do not make a strong assumption of dynamic consistency between the scenes, learning priors can be conducted in simulation to avoid collecting data in real-world circumstances. We evaluate the effectiveness of our approach in the context of contact-rich fabric manipulation, which is a common scenario in industrial and domestic tasks. Detailed numerical simulations and real-world hardware experiments reveal that our method can achieve rapid skill acquisition for challenging manipulation tasks.