I don't want to spoil my answer by reading other fine answers, so I will skip reading until later.
Who told you that the world should be free from suffering?
Not even addressing the fallen condition of man described in the Bible which necessitates "the Law" and the "ransom." Let's just go right to birth defects and child abuse and the 2004 tsunami that swept away tens of thousands of children and the 2010 Haiti earthquake that also killed tens of thousands of children and maimed others. What jerk of a god stands by and lets that happen? A "God" could have easily just caused such a thing as a tragic tsunami or earthquake to not happen rather than provide a revealed miracle.
Do you find any value in suffering?
If people got some value out of the disaster, the price was too high. The agony of parents and grandparents and siblings was too much to ask for even if all those children get some future reward. If people get some value out of knowing about child abuse, the abuse for even one child is a price too high.
Do you think it is possible to experience all the beauty and goodness and pleasure the world offers without also experiencing the bad? Isn't good only good because we know what bad is? If there was only good would it really be "good"?
I have heard that and don't go along with it. I get that challenged people do more than unchallenged people, but I don't believe we need tens of thousands of children to die so that people can appreciate surviving. We could easily discuss the beauty and goodness and pleasure that children can find in a world without traumatic and sexual abuse.
If you where God and could eliminate suffering what would the world look like? Or conversely if there was a loving God what should we expect the world to look like?
I don't typically bother with such a "what if" question because the inquisitor simply says that there are reasons my way can't be the way. But I will answer part of it. No children would be born with mental and physical defects that cause pain or extremely difficult lives. People who abuse children would be revealed in public before I would assign them to oblivion.