What are some of the "Self- Reliance" narratives that changed the American identity?

Like other American writers in the early days of the republic, Emerson tries to establish an equalitarian American identity, distinct from the European reliance on tradition and hierarchy. In "Self-Reliance," he does this in several ways.
First, he rejects merely adopting the tradition represented by European thinkers such as Plato and Milton. Instead, Emerson writes that "imitation is suicide." He backs this idea up using the American imagery of a small farmer tilling his soil:

no kernel of nourishing corn can come to him but through his toil bestowed on that plot of ground which is given to him to till.

In other words, Americans must pull themselves up by their own mental labor, as they have through honest physical labor. They must use their own brain's bootstraps, and not rest contently, in a European style, on the intellectual inheritance of the past.
Emerson helps create an American identity by leaning in on the fearlessness of change that distinguishes the American mindset, noting that the men in his audience are

not cowards fleeing before a revolution, but guides, redeemers, and benefactors, obeying the Almighty effort, and advancing on Chaos and the Dark.

The above statement seems to foreshadow the idea of Manifest Destiny, which said whites had a right to the American continent, which was characterized as dark and chaotic before they came.
Emerson also plugs into and praises an American identity of youthful brashness, defiant of aristocratic rank:

The nonchalance of boys who ... would disdain as much as a lord to do or say aught to conciliate one, is the healthy attitude of human nature.

In other words, Americans should feel as free as any European aristocrat to speak their own minds. Emerson puts this more forcefully when he states,

Kingdom and lordship, power and estate, are a gaudier vocabulary than private John and Edward in a small house and common day’s work; but the things of life are the same to both; the sum total of both is the same.

Emerson goes on to disdain traveling to Europe or Egypt to get ideas: we should stay in our own place. The one who goes to old places finds that

his will and mind have become old and dilapidated as they.

Emerson forcefully insists that every person's thought is potentially of equal value, no matter their rank in life. Don't defer to the great, he says; they should defer to you. Be vigorous and bold; trust yourself, not tradition. Don't be chained to the past. This an assertively American attitude that helped create American identity as individualistic, forward-looking, and equalitarian.