The objection to human suffering has been a big one I've seen around a lot. I often respond that we are in a broken world, but that our suffering is also not meaningless because God is working even the evil for good, even though in our finite being we may not see the whole picture.
Romans 8:28
28 And we know that God causes all things to work together for good to those who love God, to those who are called according to His purpose.
For someone who doesn't believe in God, from their worldview--even though they may not realize it--their suffering is meaningless. Because if all we are is stardust and chemical reactions in the brain with no eternal soul, we are all just waiting out this ticking time bomb of the heat death of the universe. There is no meaning to anything in this life, because once its over, there's nothing.
The other aspect of suffering is that even though God allows us to experience suffering, He is not remote from it, He is with us in our suffering. He did not exempt Himself from suffering, but died so that we would not suffer eternally. We can be with Him eternally satisfied in His eternal goodness and grace.