Thanks for sharing. That was a big issue for me too as a sceptic. I definitely don't have all the answers to suffering or anything like that.
What helped me come to a Christian worldview despite suffering and evil were a few of the following things. Not sure if this will help you on your journey but I'll briefly share in case.
1. Intrinsic value of life- one of the main reasons suffering is so bad is because we think human life has an intrinsic value but this is something that makes more sense under theism.
2. Objective moral values- there is some real evil in the world and inside all of us. Yet, I found theism the most plausible basis for objective moral values.
3. As Frankl says life either has meaning or it doesn't and by implication suffering either has meaning or it doesn't. Do I know the reason why natural random disasters are allowed happen? Far from it. But there is enough intrinsic beauty in the world and evidence for the historical roots of Christianity for me to just dismiss it outright.
4. The cross of Christ- to dismiss a Christian worldview we need to dismiss the worldview as a whole- in Christianity Christ suffers brutal death, the divine meets humanity in the fallenness and brokenness of it all.
5. Knowledge of God is an incommensurable good- there can be a purpose to things in showing different attributes of God (eg. forgiveness means something when there is evil) and our dependance on him.
6. Being real- I appreciated the approach to suffering in the Bible where we can be honest we don't have all the answers as to why things happen.
7. Afterlife- in Christianity this world is not all there is so if the view is really correct the suffering is this world will be like a minor blip in a dream. This isn't an answer to the emotional pain of suffering (I think the cross of Christ is much better for that) but an overall consideration in terms of worldview consistency.
8. Worldview consistency- I found as a sceptic I'd pick Christian presuppositions around human life, objective morals etc and use them to make a case against Christianity being true. However, at the same time I'd not bring the cross of Christ or the afterlife into the picture.
9. To say there are no morally sufficient reasons why God could allow suffering goes into the realm of sheer speculation.
I could also talk about human freedom, the fact most animals are happy most of the time, how suffering can show love and compassion at a deeper level etc etc but this will suffice for now.
I might write on this in the future.
All the best on the journey.