The first question we need to address is, "What happened that resulted in pain, evil and suffering?” The Bible speaks of a world created by God where everything was "very good." Then, through the disobedience of the first man and woman, sin entered our world and its many effects / consequences. You may be thinking, "that’s not fair, it wasn't my choice." In a sense, every person who will ever live was represented in that choice, and even if it had been Adam and you, or you and Eve, do you really think the result would have been any different? Especially considering the track record of mankind the Bible records – God calls, man responds, man forgets and disobeys God, and God judges. If you and I are honest, we have to admit we’re repeating that pattern. Sin was our choice, not God's, but the Good News is that one day, sin and all of its terrible consequences will be completely and totally eradicated. But what about the meantime?
As for the second question, "Why not eliminate pain and suffering now, instead of waiting?" While we're not told why, would you consider that if God allows it, then it could be for some greater purpose? In the Apostle Paul's epistle to the Romans, chapter 8, verse 28 he tells us:
'And we know that in all things God works for the good of those who love him, who have been called according to his purpose." (New International Version)
In a recent radio broadcast, Max Lucado made the observation that if God removed suffering, pain and evil now, then he would also have to take away our freewill and choice. However, if we’re allowed to make choices, then there will be consequences to those choices.