It's very easy for us to see how the joys in life can bring us closer to God but at times it's a bit harder for us to see how the "not so good stuff" can do the same - at times in more powerful ways than the happier aspects of life can. The conversions of most of the people I know came about through what people would consider a bad experience (or a series of them). I'm not saying that the wonderful things in life don't bring us closer to God, I'm simply stating that many people I know turned to God wholeheartedly after a series of painful events or circumstances. God transformed their pain into something good.
They "allowed" Him to. We always have a choice in our response.
When it comes to suffering of any sort the disposition of the heart can be the difference between allowing bitterness to enter the heart or allowing the Lord to transform our pain and suffering into something beautiful. We can wallow in bitterness (I spent years in this "spiritual state", unfortunately) or we can trust that God is not "picking on us" (obviously I thought this at one point...lol) but allowing certain events to happen knowing that He is going to use these events for our good. This isn't what I would call positive thinking but rather "trusting in the God of all truth and goodness". The words "positive thinking" make me a bit wary in our days because they can be used as blinders or a refusal to see truth. They can even be used as a way to avoid correction or as a way to avoid responsibility. I'm not so sure the term means the same thing as it used to. Jesus was a truthful thinker not a positive thinker. He was often very blunt in His manner of speech. When He cleansed the temple He didn't put a positive spin on it "Oh, everything is fine and dandy here in God's house so I'll just leave things be." No, He saw the "truth" of what was going on and did something about it.
Look at the Crucifixion of Our Lord. God changed the world for all time through His death and resurrection. All things were transformed through Jesus who suffered so painfully for our sake.
Jesus never said we would not suffer here on earth. In Matthew, Mark, and Luke the "conditions for discipleship" are taking up the the cross and following Jesus. After each of these Gospel passages the next passage is about the Transfiguration of Christ. A coincidence? No way.
Picking up our cross and carrying it transforms us because God made it so.