I doubt not God is good, well-meaning, kind (1)
Not a word about race in here, so how is this opening line of the poem about race? Well, it's not exactly, but it is about identity. The poem opens with "I," so right off the bat we're getting the speaker's thoughts about his subject. While identity is usually something shaped by experience, here we have the speaker taking shape through his intellectual investigations into the nature of God's relationship with man, ambiguity and his identity as a black poet. We'll say this line gets the ball rolling (but downhill, like in a good way, not uphill, like Sisyphus).
To catechism by a mind too strewnWith petty cares to slightly understand (10-11)
Here the speaker says "a" mind rather than "my" mind, but we think it has something to do with how the speaker understands his relationship to God. He says that a mind preoccupied with petty concerns can't understand God's ways. In other words, our speaker sees himself as unable to answer his questions about God. This adds a universal aspect to the speaker's dilemma. At this point, he's saying that God's reasons are beyond human capacity, but he's also saying, this includes all of us: me, you, black, white, every human being on earth. So, in that way, our speaker is no different than you or me, right?
Yet do I marvel at this curious thing:To make a poet black and bid him sing! (13-14)
Finally the speaker addresses race. While the first 12 lines of the poem addressed more universal themes like God and humanity, here the poem turns to the specific topic of race. The speaker marvels at yet another apparent paradox in the world: God made him a black poet. A sense of irony can be read into this line, as if to say, "Oh wow, isn't this crazy? I'm black and I write formal poems! No way!" During a time period when African Americans were just startling to establish themselves as serious artists in the white-dominated culture of America, Countee Cullen would've been aware of the racism that had minimized black participation in America's literary tradition.
On the other hand, the last line doesn't have to be negative, or even sarcastic at all. Despite admitting that he can't understand God's ways, the speaker still marvels at his identity as a black poet. Why is this something to marvel at? The question of identity, relationship to God and role in American culture is what fuels the speaker's desire to "sing" and so it's like just asking the question and writing a poem becomes a part of the speaker's identity.