This is not an eloquent post. Just a series of truths taken from the Bible...
Blame all suffering on Adam and his sin. This world, with all the disease and disasters, is not the way God originally made it. Romans chapter 5 says that death entered the world through Adam's sin. Adam was like a real Pandora, and his sin opened the box to let all the evils of the world flood out. All suffering is Adam's fault, not God's fault. You might blame God for creating humanity with the capacity to make a wrong choice. God could have created Adam as a machine so that he could not sin, but a machine can't love. Also, how much suffering is happening because human beings look to their false idols, and not to the one true God who is able to deliver?
God uses suffering to choke off greater evils. Humanity's short life span (compared to the superhuman life-span of pre-Noah-flood humanity) limits the number of years that evil people can do evil. God strikes down the wicked every day, which is a good thing for the over-all survival of the race. God also uses suffering to teach human beings empathy. Sometimes bad people develop a spark of care for others that they otherwise might not feel, when they suffer.
God subjected His own Son to suffering. Jesus of Nazareth is how we know God is not an unconcerned Cosmic Eyeball in the Sky. Jesus of Nazareth experienced hunger, thirst, oppression, and poverty -- poverty worse than 99% of the poor of America have experienced.
Since Christ was a normal human body, I have no reason to think that Jesus never got sick (since sickness is not in all cases, or even most cases, punishment for sin). I believe baby Jesus' nose ran when he teethed, I believe he caught a cold from time to time, and it really hurt if he hit his thumb with a hammer. He certainly suffered in every possible way. horribly, when He died. Because Jesus was God in flesh, and He learned obedience by what He suffered, you cannot say that God does not know what it feels like to suffer.
Suffering for God's people is always temporary. No one in heaven right now is angry about their own past suffering, or worried about it, or complaining about it. Absolutely no one. The apostle Paul said that the glories of eternity with our heavenly Father will make our "brief, light" afflictions here on the earth like they were nothing. We're the ones who are angry, complaining, and brooding. God's people in heaven, singing around Jesus' throne and fellowshiping with one another, aren't thinking about it at all, except about how God came through for them in the midst of it all.
No one can say that God doesn't care about suffering, when He slaughtered His own Son to put a permanent end to suffering. If you believe Jesus rose from the dead, then you also believe He's going to fix absolutely everything one day. Because He said He will.
I'm going to say this soberly, not lightly: God never promised to give Christians pain-free deaths. Death is absolutely unnatural, and our bodies fight it.
God's people have died in all kinds of ways. There are Christians who have died on the battlefield. Some have died by jumping on top of a grenade to save their buddies. Christian military personnel have drowned on sinking ships, or, during WW II, some were attacked and killed by sharks. I imagine Christians in Africa have been killed by lions or hippos. Christians die in car crashes, plane crashes, train derailments. Christians died in the Twin Towers. We know of one Christian who died heroically, forcing Muslim terrorists to crash the plane into a Pennsylvania hillside. Some Christians have died in agony from the ravages of illness, in the years before there was modern pain medication. And some Christians die peacefully, in their sleep, at a ripe old age, surrounded by their loved ones. Everyone is different. But each death is precious is the eyes of the Lord.
The Bible reveals that, among the hundreds of billions of people who have ever lived, God only spared two people the ordeal of death: Enoch (whom God took directly, we know not why), and Elijah (who went to heaven in a blazing chariot). Not even the Son of God was spared.
Death is the final exam of your faith. It is the last test before permanent summer vacation -- the eternal holiday that Jesus bought for you with His own agony. It matters little the circumstances by which we leave this place. What matters is whether we leave here in faith. God promises that eye has not seen, ear has not heard, nor has it been imagined by the mind of man, what God has in store for His children. Once you are there, you do not care how you got there.
There is a Heaven because God is good. God sent His Son, because God is good. God gives us everlasting life through faith in Christ, because God is good. God helps us get through the ordeal of these few short years on earth, because He is good. God is going to lock Satan into Hell one day, because God is good. God is going to heal the earth one day, because God is good. God is going to resurrect His children in glory, because He is good. God can bring good results out of horrible circumstances, in spite of the circumstances, because God is good.
The question is not, "if God is good then why do we suffer?" The real thing I marvel at is, Why does God do good for any of us, in light of our sins?