Most navigation approaches treat obstacles as static objects and choose to bypass them. However, the detour could be costly or could lead to failures in indoor environments. The recently developed navigation among movable obstacles (NAMO) methods prefer to remove all the movable obstacles blocking the way, which might be not the best choice when planning and moving obstacles takes a long time. We propose a pipeline where the robot solves the NAMO problems by optimizing the total time to reach the goal. This is achieved by a supervised learning approach that can predict the time of planning and performing obstacle motion before actually doing it if this leads to faster goal reaching. Besides, a pose generator based on reinforcement learning is proposed to decide where the robot can move the obstacle. The method is evaluated in two kinds of simulation environments and the results demonstrate its advantages compared to the classical bypass and obstacle removal strategies.