Contact-rich manipulation is difficult for robots to execute and requires accurate perception of the environment. In some scenarios, vision is occluded. The robot can then no longer obtain real-time scene state information through visual feedback. This is called ``blind manipulation". In this manuscript, a novel physically-driven contact cognition method, called ``Contact SLAM", is proposed. It estimates the state of the environment and achieves manipulation using only tactile sensing and prior knowledge of the scene. To maximize exploration efficiency, this manuscript also designs an active exploration policy. The policy gradually reduces uncertainties in the manipulation scene. The experimental results demonstrated the effectiveness and accuracy of the proposed method in several contact-rich tasks, including the difficult and delicate socket assembly task and block-pushing task.