Edit: I link a thread at the bottom of this answer that, if I were in a position to, I'd consider mandatory reading before even looking at what I wrote below.

“The Native Americans” is a term that leaves extraordinary scope in answering this question. The North and South American continents have been peopled with a diversity of cultures/polities with varying ambitions, varying mythologies, and varying social architectures for tens of thousands of years. To ask this in terms of “the Native Americans” is to reduce millions of people to a monolithic entity of the past, with no history or future. I don’t mean to attack the way you’ve phrased the question (because it’s a really good one); it’s unfortunately understandable, considering this (NSFW) seems to be the idea that still lives in classrooms in the United States. So with that preface, this is far from the answer to your question.

We demanded why they came in that manner to betray vs, that came to them in peace, and to seeke their loues; he [Amoroleck] answered, they heard we were a people come from vnder the world, to take their world from them.

The above is John Smith, recounting in his Generall Historie of Virginia, an interaction between himself and a prisoner of the Manahoac named Amoroleck. This answer almost certainly confirmed Smith’s own previous estimation that Indians encountering the English regarded the newcomers as gods. This, of course, is an idea that has clung to American founding mythology for centuries. Initial Indian assessment of Europeans possessing supernatural abilities is not completely incorrect, but there is far more to it than the worship of muskets and metal cookware that is popularly portrayed.

In the spirit of my first paragraph, there is something incredibly important to keep in mind with my answer: it comes from early English and French reports of Indian culture. These reports were intended for an early modern audience, among whom were prospective investors in companies that were trying to settle North America. This was often at the front of the minds of writers and artists such as John Smith, Roger Williams, Thomas Morton, and John White. Many of these depictions, such as White’s drawing of the village of Secotan, were intended to reassure readers and viewers that while the native populace of North America was indeed different, they weren’t too different. A little bit like how resorts pitch the Caribbean to honeymooners. Even the honesty that on-the-ground English did try to convey could be altered dramatically to better suit European sensibilities.

The “gods” among whom John Smith and others numbered themselves fell into the Indian concept of manitou. The supernatural (or divine) could possess all things. Manitou, thus, was not one god in particular, but a collective of unexplained phenomena with power over the daily life of Indians. Manitou could take on almost limitless physical forms. French Jesuits in pays d'en haut likewise encountered manitou. In fact, these priests were initially grouped among them, but as their limitations became clearer, this status was taken from them. The Indians expected more than European end-items from the Jesuits. With the power of a manitou should have come cures for disease, good hunting, and advantage over their enemies. Even in the conversion of Indians to Christianity, the manitou retained status. As Richard White points out in The Middle Ground, “Indians were not so much being converted to Christianity as Christ was being converted into a manitou.”

Roger Williams, in A Key into the Language of America, let English readers know that the Narragansetts regarded them as “strangers.” Wenooch was the word for the English among the Wabanaki. It was a question: “Who is that?”

The answer that Amoroleck gave to John Smith served here as well. English reports of native religious beliefs were often fitted into a context that would make sense to English stakeholders back home, and with discussions of manitou often came expressions of disgust, as in the case of Thomas Morton, who outright denied the existence of Indian religion. Reporters like Morton aside, however, English writers did try to assess Indian religions. In terms of the origins of the English, many natives expressed the same idea as Amoroleck. The English had come from the underworld. The English were dead men returned, in keeping with the idea that the dead lived again in the afterlife and eventually returned to this world. The diseases that accompanied the English (but did not affect the English) were bullets fired at the Indians from other, unseen, returned dead.

Finally, it is worth noting that such dramatic European provenance as the underworld would be refuted quite quickly when Indian kidnap victims/travelers would make their way to Europe. For instance, only ten year elapsed between the founding of Jamestown and Pocahontas’s death in Gravesend, England. By 1618, Squanto had made an Odysseus-like return to New England by-way-of-England-by-way-of-Spain-by-way-of-abduction from New England.

The two sources I’ve primarily drawn on for this answer are as follows:

Kupperman, Karen Ordahl. Indians and English: facing off in early America. Cornell University Press, 2000.

White, Richard. The middle ground: Indians, empires, and republics in the Great Lakes region, 1650-1815. Cambridge University Press, 1991.

Kupperman writes:

They [English writers] accomplished their job of gathering local knowledge and reporting their own observations so well that these accounts, incorporating native voices, are still our main ethnographic resource for understanding American societies at contact.

For problems with White’s work that are undoubtedly present in Kupperman’s, see this AskHistorians thread by /u/Snapshot52.

Lastly (I know I already said "finally"), what I'd welcome even more than this answer surviving initial mod-screening is a challenge to Kupperman's statement that is in keeping with the thread I linked above.