Massive gravity is a modified theory of general relativity. In this paper, we study, using a method in which the scale factor changes as a particle in a “potential,” all possible cosmic evolutions in a ghost-free massive gravity. We find that there exists, in certain circumstances, an oscillating universe or a bouncing one. If the universe starts at the oscillating region, it may undergo a number of oscillations before it quantum mechanically tunnels to the bounce point and then expands forever. But going back to the singularity from the oscillating region is physically not allowed. So, the big bang singularity can be successfully resolved. At the same time, we also find that there exists a stable Einstein static state in some cases. However, the universe cannot stay at this stable state past eternally since it is allowed to quantum mechanically tunnel to a big-bang-to-big-crunch region and end with a big crunch. Thus, a stable Einstein static state universe cannot be used to avoid the big bang singularity in massive gravity.