No suffering is not a necessary part of the human condition. Suffering is simply there to teach us how to end suffering. What I mean by this is that the more self-aware you become, the less that you will suffer.
Try this exercise. Take a moment to focus on your breath. Can you identify your current feelings? For example, are you feeling discomfort, pain, happiness, sadness, love, hate, anger, frustration, contentment, relaxation and forth? I want you to focus your attention deeply on what you are feeling. Feel it until it consumes you. Whether it is pain, happiness or sadness, it does not matter, focus on it until nothing else exists. There will come a point where you will feel a release and sense of peace. This is what it is like when you begin to give up suffering.
When you understand that suffering is just a resistance to what is and an avoidance of anything we judge as unpleasant, we can choose to give up this kind of resistance.