I can understand the thought that "there couldn't be a God who would let this happen." We certainly live in a world where sorrow and trial is abundantly common.
But, if there is an eternal God who loves us with an infinite love, would He let those things happen to us if there wasn't some reason for it all, and if there wasn't some way to overcome and come back from those sorrows and trials?
That kind of seems like a twisted worldview, to say that all bad things are for a reason. But I'm not saying that these bad things aren't bad. Pain, especially pain caused by other people, is not pleasant. God sorrows when his children have to endure these things, and those that cause pain will be held accountable, in one way or another.
But God has an eternal perspective. We lived as spirits before we came here, and we'll live eternally with glorified bodies after we leave. Our time here on Earth is a very small portion of our eternal lives. In the grand scheme of things, any trials we face here will seem like far too little compared to the rewards we receive for enduring them well.
Something that our religion believes that isn't a major part of any other is that, because we are literally God's spirit children, we are also his literal heirs. Those that make the vital covenants in the temple, keep those covenants, and follow the commandments are able to inherit everything that God has, essentially becoming Gods and Goddesses themselves, able to have their own spiritual children, and able to make their own worlds for those children to inhabit. Why would God place us on a seemingly insignificant speck in a vast universe, forced to suffer trial? To learn. To grow. And to become more like him, so that we can be prepared someday to take up what He has, and so that we can empathize with our own children as they go through the same thing. God put us here so we can become more like Him.
Of course, we make mistakes, or are hurt by the mistakes of others. That's why God sent his son, Jesus Christ, to suffer and die for us; so that we would have a way to repent from our sins, be healed from the effects of others' sins, and overcome our trials.
Jesus felt every single physical, mental, emotional, and spiritual pain of every single one of God's children. So he knows exactly what you're going through, better than anyone else in the whole world. He's the one that knows best how to guide you through your trials.
I've felt his love and guidance in my life. I've felt the love of God and Christ through the Holy Ghost in ways that I can't explain. I've seen things, felt things, that cannot be explained by anyone or anything else. I know this is true. I know that God loves you, and his Son Jesus Christ loves you. Jesus is your literal spirit brother. He's your older brother, one that you can rely on in any situation. He knows what you're going through, and also knows how to help you through that so that you become better on the other side.
If you've felt that, don't ignore it. Because it is true.
And please, if you have any questions about the Church, ask me, or any of us. We're happy to answer.