If people are allowed to make choices, evil is a possibility. You can argue that free will isn't good, but I'm not sure what evidence supports that argument.
So if God allows free will, then evil can happen. Just because he doesn't immediately stop it (read: eliminate free will) doesn't make God not-good.
I think part of this is man's hubris in assuming we can know what is perfectly good. The Epicurean paradox is hinged on the description of "all-good," which is far too simple in most people's minds.
A metaphor:
If I shove my child to the ground to teach them the consequences of falling, I am a bad father. If I warn them to tie their shoes, or they will fall, but do not explicitly force them to, I am a father willing to let my child learn, but I am not a "bad father" because of this.
Another aspect I think the Epicurean paradox misses is the concept of justice and eternity. If this physical life is all there is, then yeah, allowing people to suffer and die is an injustice. But if we are eternal beings in a temporary, physical body, suffering and dying in this world is a small blip on the timeline. What comes after has to be factored into the equation of "What is justice?" But that's where non-theistic reasoning can no longer come with us. The Bible is fairly clear about what comes after, and there is justice when viewed in that light.
If you believe this life is all there is, then yeah it's not hard to argue that God isn't just. But again, the Bible, upon which the Judeo-Christian belief system is built, is very explicit that this life is NOT all there is.
So the Epicurean paradox takes a small slice of the Bible out of context and points at it, without considering all the other context and argues, "Ha! See? Logical inconsistency!" when in reality it's just out of context.
I think free will can be attributed only to actions people are doing. But not everything can be attributed to people (or other animals).
Even without the theology, a person suffering due to a forebear's poor decision is well-understood: a decent percentage if people think it's the natural order for a child to go hungry if their parents are drug-addicts or imprisoned.
If someone gets cancer as toddler who's fault is that? If someone is born with disability, with caused by new mutation, who's fault is that? Are these part of free will? Do you thing that it is good that it is happening?
The Bible is not very clear about what happens with an afterlife. The book of Revelation is where you find the most intimations of divine judgement, but the OT has little to nothing and many Biblical scholars agree that the idea of end leans heavily towards the Jewish idea of a literal heaven on earth for the chosen people and that's all.