Knowing that something is possible is an important piece of information in working to bring that something about. When the Buddha achieved liberation, he demonstrated that liberation is possible. Knowing that liberation is possible is itself liberating.
The belief that it is possible to end your suffering, takes the edge off your suffering. It is only your perception that causes your pain. When you believe that, then you begin the process of questioning your perceptions. See how they create the conditions of suffering with anger, desire and ignorance. Ignorance in the Buddhism sense is an inability to see impermanence and a belief that things and people exist independently of each other.
If you believe that the Buddha achieved liberation, then you have to believe in your own delusion. Recognizing your delusion, accepting your ignorance, is a part of your liberation. The greatest part of the Buddha’s discovery is that liberation is possible for anybody. That’s really something.