I believe this is one of the most challenging questions to answer because it's so painful to see such terrible suffering in the world that occurs especially when it's at no fault of the suffering soul. Therefore, this question requires a sincere answer in response to the emotions it invokes as well as the possible contradiction posed by Epicurus.
In response to Epicurus; he makes a fatal error in his logic by not considering the possibility that God has a sufficient reason for allowing such suffering in the world. If this is even possible it completely eliminates any logical contradiction concerning the existence of a good God and the existence of evil. In God's omnipotence He can choose to allow terrible things to occur in order to bring about a greater good later. Think about the story of Joseph (Gen 37-50), or, most importantly, the betrayal of Christ which brought about atonement for our sins. In this past century alone, our world has seen the most despicable dictators such as Joseph Stalin, Pol Pot, and Saddam Hussein to name a few. Even in the face of the massive killings of China people are rushing to the Lord at a rate faster than any where else in the world. In Pakistan you can receive the death penalty for conversion yet they still are unable to stomp out the forest fire of belief in Christ. In Africa, from the early 1900's to date, the population has gone from less than 5% Christian to around 50%, in the face of famine, raping and brutal murders. God exchanges the suffering of the world, not only for many good things, but also for His most cherished affection, which is us.
Some may say if God is Omnipotent (all powerful) then why not just eliminate evil altogether and let us live in happy harmony. I suggest this premise has not been thought through very carefully for if God's standard is perfection He would ultimately have to either revoke our free will or eliminate all mankind since we have all fallen short of His glory (Rom 3:23) and deserve death (Rom 6:23). Even the atheist must admit that he has committed some evil according to God's standards, thereby qualifying for elimination. But as we have seen, God doesn't want to eliminate us but wants all people to be saved (1 Tim 2:4).
What about the children who die before being baptized, where do they go. I would first like to say that although Jesus commands a professing Christian to be baptized, he never requires it for salvation. In fact, he tells the criminal on the cross next to him who had a repented heart, "Truly, I say to you, today you shall be with Me in Paradise" (Luke 23:43). This thief did not have the opportunity to be baptized yet Christ is telling him he will be in heaven. I would also like to point out in contrast to the Christadelphian claim, that the bible indicates here and in Luke 16:22 that believers will indeed be in heaven immediately after dying. Romans 10:9-13 tells us how to be saved and baptism is not part of it. Furthermore the bible indicates that a child who dies goes to be with the Lord. (2 Sam 12:23) When Davids son dies he says, "I will go to him, but he will not return to me", meaning David will see him again in heaven. And again in Ezekiel 16:21 God calls the young children of Israel who were being sacrificed by fire, His children, and we know from John 1 that to be a child of God is to be saved.
Lastly, about the people who are unreached by the gospel before there death. Read Romans 1 and 2 very carefully and you will find that although a man may not have heard the gospel he still has the testimony of God's existence from creation and an inner conviction (also see John 16:8). This conviction is the same conviction that drives any person to repentance. Christ is not limited to just using people to share the gospel, he can do so by coming Himself to a believing and contrite soul, in a vision, as he has done for so many people already. Many Muslims who have come to Christ will testify that they were met by Christ having never heard the gospel a day in there life, Amazing!! Read Acts 10 and you will see the story of a man who loved God but never heard the Gospel, and God sent Peter to him so that He may hear.
I hope this makes sense, I know it's very long answer but these are questions that many have written entire books about. I really hope and pray that you would reconsider your disbelief. Think about this, you lost your faith because of all the injustice going on, meanwhile the people being treated unjustly are gaining such strong relationships with God. James 1 was written just for these people to remain strong during trials, and I plead with you to do the same.
