I think one prominent truth that is established in section one (and carried out throughout the rest of the poem) concerning Whitman's view of "self" is that although he is speaking about himself (this is definitely an autobiographical/philosophical poem), he does not speak for himself alone. This part is made obvious in the last line of the first stanza:
And what I assume you shall assume,
For every atom belonging to me as good belongs to you.
Besides the evidence that "self" is supposed to be a collective word, in this first section, Whitman next establishes a tone of appreciation for life - the fact that he did not come from nothing and thankful for the things that he is made up of. In this way "self" is not selfish but rather, a grateful self that knows where it came from.
Finally, Whitman establishes a very obvious tone that death is inevitable.
I, now thirty-seven years old in perfect health begin,
Hoping to cease not till death.
The majority of the rest of "Song of Myself" revolves around this idea - the inevitability of death as a reason for appreciating life. By using the idea of "self" - Whitman shows how he considers all men (mankind) to be connected through the element of death, and as a result, we should all be thankful for life - and live it to the fullest.