May I ask why pushing a table by hand does not work in the beginning, when the object can be pushed when the force is constantly increased, and then the more it is pushed, the easier it becomes.

Starting to push, one is to overcome the role of static friction, the second is to make the stationary object to move to have an acceleration, which requires a larger thrust.

After the movement, such as the need to accelerate, as long as the sliding friction can be overcome. The thrust required is less than that required to move the object in the first stage.