Now, we don't tend to think about the Biblical story this way. We tend to think of theodicy--the problem of evil--as a particular theological issue rather than the grand plot of Scripture. Theodicy is a niche subject, a specialized conversation, not the whole story itself. But really, the drama of the Biblical story is, in its entirety, a theodicy. The Bible tells the story about why evil exists and what God is doing about it.
Why is there evil? The Bible starts off with an answer, what we call "the fall" of Adam and Eve. There's another fall in the background as well, the fall of the rebellious angels and cosmic archons, the "principalities and powers." This "double fall" is the explanation given by the Bible for the question "Why is there evil?"
As to what is God doing about evil, well, that's the main plot of the rest of the Bible, isn't it? Facing the ruin of human and angelic rebellion, God acts in history through Israel and Jesus to eradicate evil now and in the eschatological healing of the wounded cosmos.
My point is that the questions raised by "the problem of evil"--questions like "Why is there evil?" and "What is God doing about evil?"--simply are the story the Bible is telling. Now of course, we might have a lot of follow up questions. For example, why did God create the angels if he foreknew their rebellion? Or, why does God chose to deal with evil through Israel and Jesus instead of just acting directly against the evildoers? These are valid follow-up questions, but my point is that they are follow-up questions. The Bible has already given you an answer to the problem of evil. You might not like the answer, or have a lot of questions about the answer, but you do, in fact, have an answer.
Maybe all this seems obvious to you, but maybe it doesn't. For example, I've heard theologians say, "The Bible doesn't provide us with a theodicy." But given what I've just pointed out, that's a very strange thing to say. Because the Bible, in fact, does provide us an answer to the problem of evil, or at least a story about where evil comes from and what God is doing about it. Again, you don't have to like the answer, but you have an answer. You've been given an explanation.
I think we often miss this point because we tend to fixate "the problem of evil" on the word "allow." As in, why did God allow evil to enter the world? And, why does God continue to allow evil to exist? Unfortunately, answers to the "allow" questions we just don't have.
We do, though, have answers about the origin of evil, God's response, and the final destiny of evil. Perplexities persist, of course, but the Bible does give us answers to many of the questions we ask. I'm not saying that we like, understand, or can believe in those answers. I'm just pointing out that many seem to assume that the Bible is either silent, dodgy, murky, or mysterious on the topic of evil when, in fact, it's sharing answers with us loud and clear.
Framed this way, the "the problem of evil" isn't the lack of a theodicy but, rather, our posture toward that theodicy. The "problem" is that we just don't like or believe the story.