The speaker metaphorically compares the human spirit to an unsharpened tool—a "blunt," or dull/clumsy—"instrument." Such a tool, the speaker says, couldn't possibly "have made this baby."
Readers might picture the speaker holding their own baby as they marvel at the "intricate" perfection of the child's body, which the poem presents as akin to a carefully crafted work of art. The "spirit" is like a hammer or dull knife clumsily thwacking away at a block of marble or wood; the creation of something as delicate and detailed as an infant requires much more dexterity and finesse than the spirit can muster.
Alliteration and intricate consonance contribute to the speaker's emphatic tone. Listen to the bold /b/ sounds in "blunt" and "baby" and to the sharp, crisp /n/ and /t/ sounds throughout the line:
The spirit is too blunt an instrument
There's also subtle assonance between "made" and "baby." Altogether, these sonic devices make the poem's opening lines striking and memorable.
Notice, too, that this first line is enjambed:
The spirit is too blunt an instrument
to have [...]
The poem pushes the reader swiftly across the line break, leaving no time to question the spirit's supposed "bluntness." Line 2 then comes to a clear pause with the full stop after "baby," adding a sense of firmness and finality to the speaker's argument.
The speaker expands on this argument in the following lines. Human "passions"—people's emotions, desires, etc.—are far too clumsy and inept to create a baby's "intricate / exacting particulars." A baby is made up of a multitude of tiny parts, in other words, each of which demands perfection. "Human passions" are messy and imprecise, and they thus lack the metaphorical dexterity to craft something so incredibly detailed.
Listen to the crisp /p/, /t/, and /k/ sounds in these lines, the sharpness of which evokes the dexterity being described:
Nothing so unskilful as human passions
could have managed the intricate
exacting particulars: [...]
Lines 3-5 are also all enjambed, giving the poem a burst of momentum and excitement that perhaps suggests the speaker getting wrapped up in the wonder that is the baby's body.
This speed is then curtailed by the pronounced caesura in line 5, which is created by the colon after "particulars." This dramatic pause signals to the reader that the speaker is about to launch into a list of the "particulars" that make up the body of this amazing, newborn human being.