There are two kinds of Christians: those of experiential faith, and those of theoretical faith. Those in the former category encounter God directly, and know - not merely believe - that He exists, even if they encounter things that are troubling and contradict their preconceptions of God.
If you are like most Christians, you fall in the latter category; in other words, you are not a mystic. For you, God’s existence is a persuasive theory, not a personally-experienced truth. You may have been swayed by the arguments of philosophers like William Lane Craig, but you have yet to attain the direct insight of mystics like St. Seraphim of Sarov.
As a corollary, your faith has probably been shaken at least once in your life by the reality of human suffering. This is understandable; any theoretical Christian with a shred of compassion will acknowledge that such heartrending manifestations of suffering as the dying child can be a huge stumbling block to one’s faith. Indeed, I would prefer the atheist whose compassion for others drove him to disbelief to the theoretical Christian whose indifference to suffering explains why he has remained steadfast in his faith in spite of it.
From a strictly rational perspective, however, suffering cannot be taken to be a stand-alone reason to doubt God's existence.
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