Although we don't necessarily get images of God in this poem, the speaker uses his belief in God's goodness as a building block for his argument that there are things in life that aren't always easily explained. One of those things is a good God who is immune to our cares and who has an "awful mind" and an "awful hand." Although this image of God is a bit abstract, it's a vital component of the speaker's thoughts about his own identity.
Line 2: Here God has to "stoop." Not much to say here except that the speaker is describing God as someone above us, otherwise why would he need to stoop in the first place? But there's something else at work here, too. Ever heard "don't stoop to their level" in reference to avoiding ignorant taunts by people just looking for trouble? Well, God's stoop could be like that, too. It's not that we're taunting God, but he'd have to lower himself to our intellectual abilities in order for us to understand why apparent suffering exists in the world.
Line 9: God is immune from our minds and our petty cares. Are we really that bad? Not really, but the speaker is describing God as someone above and beyond us, and despite our pleading, He won't explain away the confusing things in life.
Line 12: The speaker says God has an "awful brain" and an "awful hand." To put that in context, he's saying our limited understanding of suffering in the world makes God seem awful. In other words, it's true, God seems cruel sometimes, but we know he's not (at least, the speaker doesn't think so). But describing God as "awful" lets us in to the idea of paradox, confusion and misunderstanding that plays into the speaker's declaration that he marvels at his own existence as a black poet created by God. Plus, "awful" is a word with multiple meanings, one of which is awe-inspiring. And if you really do believe that God is good, as our speaker seems to, well then there's no doubt that God is awe-inspiring as well.