As others pointed out here, poetry was probably as close to Western philosophy as New World civilizations got. Many of these poems did concern deep existential questions, and so they can give an insight into the philosophy of ancient peoples. But they're not really phrased as philosophy in the Western sense of the word. There's not really any evidence for codified philosophical "schools of thought" the way you had in ancient Greece, for example. The Aztecs have one of the largest collections of indigenous poems that has come down to us, and I'd recommend the book Fifteen Poets of the Aztec World by Miguel León-Portilla. That book gives a great summary of the poems and a mini-biography on the poets to whom they are attributed. Here's an example of my favorite poem, supposedly attributed to King Nezahualcoyotl of Texcoco:

All the earth is a grave and nothing escapes it, nothing is so perfect that it does not descend to its tomb. Rivers, rivulets, fountains and waters flow, but never return to their joyful beginnings; anxiously they hasten on the vast realms of the rain god. As they widen their banks, they also fashion the sad urn of their burial.

Filled are the bowels of the earth with pestilential dust once flesh and bone, once animate bodies of man who sat upon thrones, decided cases, presided in council, commanded armies, conquered provinces, possessed treasure, destroyed temples, exulted in their pride, majesty, fortune, praise and power. Vanished are these glories, just as the fearful smoke vanishes that belches forth from the infernal fires of Popocatepetl. Nothing recalls them but the written page.

Sarmiento de Gamboa, one of the Spanish chroniclers documenting the Andean people and the Inca, attributed a poem to Pachacuti, the ninth Sapa Inca (emperor) of Tawantinsuyu. On his deathbed he stated:

I was born as a lily in the garden, and like the lily I grew, as my age advanced

I became old and had to die, and so I withered and died.

Besides this poem Pachacuti is known by people today as the great hero of the Inca Empire, the emperor that began the conquests. Betanzos states he took twenty years to redesign and reconstruct Cuzco as the heart of the empire before beginning his conquests, and is also credited with single-handedly designing the social, political, and religious aspects of Inca life.

Now, this has gotten some skepticism in recent years from scholars, as there are a lot of accounts that, in Terence D'Altroy's words, "unabashedly burnish" Pachacuti's image and make him the sole architect of everything Inca. However, considering the meteoric rise of the Inca state at the hands of an aggressively conquering general, the Inca certainly had philosophers, architects, statesmen...the only problem is that many of their joint accomplishments were attributed to only one man.

This doesn't really answer your question in terms of individual philosophers, but this article is really interesting and at least in the same vein as the other answers

Aztec Political Thought

We might say that the theatre state at Tenochtitlan was primarily organized not to provide security, prosperity, or even glory, but for producing transcendental experiences. In this setting, Mexica priests were, in Clendinnen’s felicitous phrase, “impresarios of the sacred” (p. 242), practitioners of the only art that really mattered in the polity, and capable of setting in motion all of its resources for the sake of producing such collective experiences. Their “work” involved not just sacrifice, but a whole series of techniques, from fasting to powerful hallucinogenic drugs to chanting and dance, designed for maximum emotional effect. (There is a great deal of interesting “psychological engineering” in Mexica ritual, and I occasionally wondered idly about the genesis of such complicated practices). And the overall effect of their work was a “calculated assault on the senses,” that contrived by very different means, the kind of delirium that we associate not with high reverence but with Carnival. Through the chant when the priests spoke in the voice of the gods and the people replied; the swirling movement of processions and the slow turnings of the dancers in the flare of the pine torches; through the long preparation, the long isolation from the routine in the fasting period, the distancing formality of the painting and robing; through the patterns of dance and drum and song etched into the senses and graven into the muscles of throat and calf and thigh, came a shifting in awareness and of the boundaries of the self. And only then, as the self evaporated and the choreographed excitements multiplied and the sensations came flooding in, did the god draw near (p. 258; I could quote Clendinnen all day).

I would recommend looking into Nezahualcoyotl for the Aztec. He is the most famous I know of.