OK, cool. In that case, I can answer it as a 'how do Christians internally justify this to themselves within their own worldview?' sense (at least for myself) - but like I said, it won't be a very satisfactory answer from a 'convince me your view about the universe is the correct one' sense.
so first off: none of the conventional 'here's the answer!' explanations for the problem of evil sound convincing to me. For evil caused by humans deliberately acting evilly I suppose you can argue human free will, but there's still what we'd call 'natural evil' - the floods in Pakistan right now, and the wildfires and plagues and horrendous painful diseases and so on and so on. I know some people believe that they are all there to teach us a lesson, or serve some greater purpose, but this does not seem very convincing to me. Some people say it's more because God can't micromanage every situation by swooping down and intervening to e.g. make that match not start that fire, because then the universe wouldn't be a predictable place we could learn in and study through the laws of nature, but again I do not find this massively convincing as it seems to be limiting God's ability to set up the universe in a way where it contains less misery in the first place.
So I don't have an explanation for why a loving God would allow this, or would create the universe in this way, and therefore I don't know. Presumably there is an answer my limited human mind can't understand, in the same way that seahorses can't understand algebra? I can't imagine what it would be, though. The world certainly has a lot of pain and misery in it.
But where I would differ from an atheist is that I already do believe in a loving God, for a bunch of other reasons. I'm not deciding what I believe in based on the existence of painful diseases or natural disasters, I'm looking at the painful diseases and natural disasters from the perspective of already having that belief, and therefore another slightly different question is: so how does that fit? how can this loving God be reconciled with all this evil? If I do not have a neat pat explanation that says "ah well, it's all part of the same thing" or whatever, then how, lacking that explanation, can I fit these two things together? Okay fine if my limited mortal mind cannot understand the greater whatever here, but my limited mortal mind still has to live with it, and I can't pretend the evil's not evil but at the same time I can't argue myeslf out of the existence of God, so... ???
And Christian theology on that point - on the point of how a loving God co-exists with a natural world full of evil, rather than the why - does give a framework for thinking about it. Because it's a how rather than a why it comes in the form of stories and analogies and narratives - which again, if you're coming from a Christian worldview in the first place, is the way that you fit "things that the limited mortal mind can't understand" within the space of a limited mortal mind. So this is why we think Jesus talked in parables - they're not like Aesop's fables - they're using narrative to say "I can't explain to you exactly what this thing is, but this is what it is like."
And the Christian narrative for what a loving God existing in a world of suffering is like, is that it's a God who does not conquer the suffering but experiences it - who does not come in as a warrior at the head of an army, but as a newborn baby born to poor teenager in a backwater of the Roman empire - who got nailed to a cross and didn't break free like the Incredible Hulk, but died. And then came back to life. So the way God defeats suffering is not to wade in and fix it and remove it and conquer it but rather suffer it, in all its horror, and then be on the other side of it. That isn't an answer to 'why would God allow this universe to run in this way?', but is some kind of answer to 'what sort of narrative tell us what it is like for God to coexist with suffering?'
It would be totally reasonable of you to say "yes but I'm not interested in that question, and I don't really care about narratives and parables and just-so stories, I want an answer to the problem of evil which would convince an atheist (or an agnostic or a spiritual-but-not-religious deist)". But I'm not trying to convert anybody and I can't really answer that 'prove me wrong, then' type of question even if I was. I can only answer the question about how I, as a Christian, live with the sense of a loving God and a universe full of evil.
(or I'm just turning my brain off so I can believe fluffy comforting stuff - people can believe that if they want I suppose!)