It would take a better informed scholar than me to say who first articulated the problem of evil, which can be stated: If God is all-powerful, he can prevent evil; if he is all-good, he would not want evil; but evil manifestly exists.
Perhaps the first was Epicurus, who concluded that therefore God does not exist. It is a simple and elegant resolution of the paradox, but of course unsatisfactory for the theist.
And so theistic philosophers and theologians have been wrestling with the problem ever since, without resolution. A zillion words have been written on the subject, to no avail. The Manicheans, at least, had a reasonable solution; God is not all-powerful (he is opposed by an equally powerful force for evil). Most contemporary theists assume that God allows evil because human freedom is a greater good (no freeedom without choice), which does not quite explain why bad things happen to good people. Others assume that God has his own inscrutable reasons for allowing evil, which begs the question. Which brings us back to Epicurus.
The 17th-century philosopher Pierre Bayle had reason enough from his own unhappy experience to appreciate the problem of evil. He was a French Protestant (by birth) caught up in the intolerance that followed the revocation of the Edit of Nantes. He wrote: "Man is wicked and unhappy; everywhere prisons, hospitals, gibbets and beggars; history, properly speaking, is nothing but a collection of crimes and misfortunes of mankind." He struggled mightily with the problem, and ended up, it would seem, somewhere close to the modern skeptic's doubt. Religious naturalists can claim him -- with Epicurus -- as a predecessor, even though his muddled and often contradictory views on religion and God have puzzled historians of philosophy. Maybe the muddle is why we like him. He certainly tried to understand all sides of every issue, and was (more-or-less) a champion of individual conscience and religious tolerance. Hume seems to have been influenced by Bayle, and did a better job at making skeptical naturalism respectable.
Religious naturalists, like all humans, are afflicted by evil and seek to ameliorate its effect by the conscious application of the Golden Rule. But we don't have a Problem of Evil to explain away. Nature is what it is, good and bad, order and chaos. Death and tribulation are a driving engine of complexification and, ironically, the evolution of moral consciousness. Most significantly, religious naturalists do not pretend to perfect knowledge, and certainly not to knowing enough of ultimate reality to suppose the existence of a personal God who is all-powerful and all-good. We are inclined to believe with Pierre Bayle and Epicurus that those popular religious beliefs that give rise to the Problem of Evil are based more on insufficently critical credulity than on reason or reality.