If there were no God then suffering would be without meaning, without the possibility of redemption. It would be suffering for the sake of suffering.
The problem of suffering in our world is that it is not God's will for it to occur but rather that His will allows it to occur because only He or through Him and good be made of it. In the case of man-made suffering, it is us through our perversion and abuse of free will who inflict suffering on others (and ourselves) – sometimes intentionally and sometimes not.
With nature, there are theologians that hold to the belief that due to the systems present in our world and the fact than man was created long after the plants and animals, that death and weather events, etc. were present. It was God's preternatural gifts to Adam and Eve that preserved them from knowing this suffering until after the fall.
Ultimately, as a Christian, I can only say that if God didn't exist neither would the we, the world or the universe.