The robot position speculation, which determines where the chassis should move, is one key step to control the mobile manipulators. The target position must ensure the feasibility of chassis movement and manipulability, which is guaranteed by randomized sampling and kinematic checking in traditional methods. Addressing the demands of agile robotics, this paper proposes a robot position speculation network(RPSN), a learning-based approach to enhance the agility of mobile manipulators. The RPSN incorporates a differentiable inverse kinematic algorithm and a neural network. Through end-to-end training, the RPSN can speculate positions with a high success rate. We apply the RPSN to mobile manipulators disassembling end-of-life electric vehicle batteries (EOL-EVBs). Extensive experiments on various simulated environments and physical mobile manipulators demonstrate that the probability of the initial position provided by RPSN being the ideal position is 96.67%. From the kinematic constraint perspective, it achieves 100% generation of the ideal position on average within 1.28 attempts. Much lower than that of random sampling, 31.04. Moreover, the proposed method demonstrates superior data efficiency over pure neural network approaches. The proposed RPSN enables the robot to quickly infer feasible target positions by intuition. This work moves towards building agile robots that can act swiftly like humans.