"Try to exclude the possibility of suffering which the order of nature and the existence of free-wills involve, and you find that you have excluded life itself." C.S. Lewis, The Problem of PainGod created us to be the objects of His love. In order to love us He had to create us with free will because to love or be loved one must have a choice. In order to have free will, the option to choose badness must exist. And, because God is just, if we choose badness, it will cause suffering.
Gepetto created Pinocchio out of his desire to have a son. Before Pinocchio became a boy, Gepetto's love for Pinocchio was a love not really realized. Once Pinocchio became a boy, he had free will, including the will to do wrong. Pinocchio choose to do wrong, and he suffered because of it.
If Gepetto really loved Pinocchio wouldn't he have protected him from suffering?
The simply answer is, "no." In order for Gepetto to fully love Pinocchio and for Pinocchio to experience Gepetto's love, Pinocchio had to become a boy. In order for Pinocchio to truly be alive, he had to be a boy with a free will. And once free will is involved, it necessarily entails suffering, because the alive person will, at times, choose to do wrong.
It is no different with God. In order for us to really be alive, we must have free will. In order for us to truly be able to feel and express love, we must a free will. And if we have a free will, there naturally will be suffering because, at times, we will choose to do wrong.
It is not God's fault that there is suffering. Suffering exists because we have a free will. We must have a free will in order for us to be truly alive, and to truly feel God's love.