I doubt not God is good, well-meaning, kindAnd did He stoop to quibble could tell why (1-2)
Right off the bat our speaker addresses his ideas about God: He's good, well-meaning, kind. So, the speaker knows God's a good guy. Furthermore, he knows God could explain all the ambiguity and hardships of life if he wanted to, but, this version of God is keeping hush about everything. So what's the idea here? God is good even though the speaker can find examples of God's apparent cruelty.
Why flesh that mirrors Him must some day die (4)
God is the big H here, and this line points out what seems like a contradiction. If God made us like Him and in his likeness, then why do we have to die? Seems like a bummer deal, right? What's so great about a God that kills off his own creation?
But the speaker is also emphasizing his inability to grasps God's ways. While he knows God is good, he can't understand what God does. This will come into play later, when he finishes the poem with a personal declaration that he's in awe of his identity as a black poet created by God.
Inscrutable His ways are, and immune (9)
God's mentioned here again and this time He's beyond reproach. He's like the king, the boss, the Don, the big Kahuna in charge who can't be corrected or questioned. This view of God as "inscrutable" actually supports the speaker's joy at being a black poet. If God made him that way, then surely it's a good thing, right?