Second there are those who simply don't see a need to care about whether God exists. They are content with his silence and see no need to question it or make inference. God's silence just means he doesn't talk.
Third, there are those who see God as alive, who have experienced something that can only be categorized as a God who, as when he spoke and light shined forth in the darkness in explosive creation, also spoke to their entire being an explosive life-giving light. There is created then a dependence, to one degree or another, on this life-creating God. As a child with a parent learns to be dependent on them for every step of life. Then at some point, they cry out ... and no one answers. And then day after day there is no answer and the weeks turn into months. God is silent. Why?
We have recently come out of a long stretch of time (almost 3 years) where it felt like God was just silent. We look for direction one way or the other and there is no answer. We know and hold onto some certainties about direction in life that God had brought us to 5 years ago or so, and yet nothing happens; no progress ... just ... waiting. Sometimes prayer and reading his word almost seem too much because such faithfulness doesn't seem to get anywhere and results in more frustration just from the resulting silence. Then one day, a glimmer of light shone through the clouds and not only did God act, but life became a whirlwind. God showed up in such a decisive way that it seemed like he had his arms around our shoulders. (Though, not like life just turned hunky-dory.)
In reflection, there are a few decisive shifts in our perspective; life-lessons if you will. First, it is very easy to get attached to the notion that such suffering should somehow be alleviated by our faithfulness to God. But he promises no such thing. All such things are according to his will and timing. We are to simply be faithful.
On the flip-side, it's easy for the idea to be embedded somewhere that some sin of ours caused such silence. That we are somehow responsible to some degree. While this may always be true on some broad level, it is dangerous to attach some tit-for-tat notion to God's dealings with man. Sometimes you can be a generally righteous person and you get the short end of the stick (read Job); and vice-a-versa. But God doesn't owe us a thing. And while we may know that in our own personal theology, living it daily isn't easy.
With this in mind, it is imperative during such times to eschew self-deprecation as if God isn't helping you because there is some insidious sin that is rearing it's head that makes God turn away from meeting your petitions. Sometimes God's accomplishing his purposes for your life has nothing to do with you (so to speak) so stop trivializing him and putting him in a box. He's bigger than that!
I think more often we simply need to be taught. God is silent because he is making and shaping us into new people. And turning our thoughts to this we should praise his silence, knowing that he has made and considered us worthy to suffer for his glory and our transformation, that he should work with us to change us and use us rather than simply abandon us.
How long, O Lord? Will you forget me forever?
How long must I take counsel in my soul
Consider and answer me, O Lord my God;
But I have trusted in your steadfast love;
I will sing to the Lord,