"Not Waving but Drowning" opens in deadpan style, with Smith immediately introducing both the poem's main theme (about communication and misunderstanding) and its main character (the "dead man"). Readers don't yet know where exactly this "dead man" is, though the poem's title suggests that he is in a body of water.
This first line also sets up the poem's central paradox—the attempt (in vain) by the dead man to explain his situation. The tense here is striking: the man is already presented as "dead," yet he is "still ... moaning." On the one hand, the use of the word "still" suggests that maybe the man still could be saved, if only someone were listening. The finality of the man being dead, however, contrasts with the urgency of "still" and creates an uneasy sense of futility. Even though the man is "still" moaning, it is too late to do anything about it; he will moan and moan, and nothing will change.
The word "still" can also be thought of as linking the dead man's moaning across different points in time—between his death and this weird, limbo-like afterlife he seems to now inhabit, and then also between the poem's present moment and this man's his entire life (as referred to in line 11 with "I was waving much too far out all my life"). In other words, perhaps the man has always been "moaning."
Moaning can mean two different things here, and Smith allows for both definitions. It can refer to complaining, which is certainly relevant to the dead man's frustrations with being misunderstood, but it also relates to sounds made in pain. The seeming contradiction between being "dead" and "moaning" can be understood as representative of the unheard expressions of pain from people who are suffering and in need of help. These cries are of no use because no one can hear them, but the doomed cry out anyway.
Alliteration in the first phrase—"Nobody heard him"—gives the line the sound of breathlessness and of exasperation, both of which are relevant to the dead man's situation (breathlessness because he drowned, and exasperation because he is/was frustrated at people's inability to understand him). There's also some consonance on the /m/ sound in these first lines, which links "him," "man," and "moaning"—essentially connecting the man directly to his agony.
Finally, the opening also puts the reader in a kind of privileged position in the sense that they can understand what the dead man is trying to communicate—while the gathered crowd within the poem itself are none-the-wiser.