Yes! Multiple groups did, in North, Central and South America. But first, a word on new and group... When talking about the genesis of "groups" or communities, we could be talking about more than one thing. This could mean new political organizations (i.e. the United States could be argued to be a "new" group compared to British or other European groups, despite having the same language). It could mean new communities or belief systems (such as the Quakers or Mormons) or it could mean something like a new "ethnic" group with strong cultural distinctiveness, or varying degrees of some or all of these. When looked at broadly, it's fairly easy to see that almost any community could be called "new" under one definition or another within a few generations.

Under new political organizations, the necessity to respond to changing political, economic and environmental challenges resulting from the arrival and expansion of Europeans in the continents resulted in many new organizations and alliances that had serious impacts on communities to where could clearly be seen as "new" to their grandparents.

Here's a few examples:

-- The Iron Confederacy of the Cree and Assiniboine took on the role of controlling much of the fur trade that went on in the prairies, and following smallpox brought in the Metis and Saulteaux as well. These four nations became one, blending communities, territories, and resulting what was very clearly a new organization and new communities.

-- Following smallpox on the British Columbia coast, the Nuxalk speaking peoples did an extensive political restructuring, with dozens of arranged marriage, all in an effort to unify the entire nation in an effort to prevent the death of lineages and ensure the community's land and food security. Although all this work was done within the traditional governance model, the resulting community was very much a new thing.

-- To give an example from further south, the Seminoles were the result of pre-existing communities supplemented by run-away slaves and others who joined them. The community that resulted would have both reflected the values and qualities of the pre-existing community that led them to accept these arrivals, but have also been changed by the new arrivals, resulting in something both old and new.

In other cases new languages resulted from these changes:

-- in the mid to late 1700s, the mixed blood offspring of HBC trappers and NWC trappers began to develop their own shared identities that gave them a common identity with each other in addition to their family relations with the communities of their mothers and fathers. This resulted in the broadly two communities known as the Half Breeds and the Michif, which have united politically since the early 1800s and today are known as the Metis (I myself am a part of this community). We were broadly multilingual, including two languages purely of our own, Michif and Bungee, of which Michif is still spoken (I am a speaker).

-- Following the American invasion and oppression of American Indian groups in the Pacific North West, a number of nations were all forced onto a single reserve in Oregon, called the Conferated Tribes of Grand Ronde. Speaking some 14 (I think?) different languages, they took to using Chinook Jargon as a lingua franca, quickly expanding it into a very effective creole, creating a new linguistic community.

These are just a couple examples of new groups forming, yet they can all be also seen as being old groups, in that they by and large function within the ongoing political/social world they emerged from. For example, Metis may have a recent origin, but in our philosophy and worldview, we are very much Aboriginal, so while we are "new", we are not out of place.

These examples don't even get to all the ways in which new identities have been imposed on people since the arrival of colonization. The creation of class systems based on blood heritage in the Spanish/Brazilian systems of colonization absolutely has resulted in new groups or in significant changes, and there are other new languages in South American that are just as cool as Michif (a language with all Cree verbs, and mostly French nouns). In Bolivia for example there is Media Lengua, another mixed language, quite young, that has resulted in a new linguistic community (though still clearly seen as being Indigenous, even though the language is mixed).

The history of groups is one of constant change, movement, as well as some degree of everpresent continuity, resulting from some degree of self-determinism. This means that change and genesis are a constant, resulting in "new" communities, yet the connection to the worldview, the connection to the familial and community ties, can mean that a "new" community can emerge, but still be clearly identifiable as "American Indian" or indigenous, and these sorts of things have happened many times since the arrival of Europeans in the Americas.

In general terms, nearly all native groups in the Americas may be termed “coalescent societies”— that is, former tribes and polities that have unified in the crucible of the pressures of colonization. Some of this, of course, occurred before “contact”; but the extreme challenges faced by native people in the era of colonization led to widespread disruption and realignment of traditional cultures & identities. The work of Robbie Ethridge ranks among the best in illustrating this process. Her term “Mississippian Shatter Zone” refers to the decline of the Mississippian era in the US South and the domino effect of destabilization felt ever since De Soto’s entrada across the region in the 1540s. I recommend her work, “From Chicaza to Chickasaw: The European Invasion and the Transformation of the Mississippian World.”

One coalescence in the South was that of the Catawbas (now in South Carolina). In the 18th century, chaotic effects of the Indian slave trade, the onset of epidemics, the regional extirpation of whitetail deer populations due to overturning for the skin trade, and other factors led to this formation of a new polity/identity. Particularly after the bloody Yamassee War (1715-1717), the Catawba coalescence took shape, combining elements of the Esaws, Saras, Enos, Cheraws, Waxhaws, Usherys, Sugarees, Sissipahaws, Waterees, and Shakoris. Many of these smaller groups left their native areas and settled together along the Catawba River which spanned across the Carolinas.

Even the Cherokees, who retained perhaps one of the strongest senses of ancient identity, and were somewhat insulated from the early cycles of destabilization due to their relative isolation, were also a coalescent group. Of their 7 traditional clans, the Long Hair clan consisted of outsiders, captives, and adoptees. Generally, Southern Indians had similar fluidity when it came to creating kinship with former outsiders, whether they were refugees seeking protection or captives taken in war. And it’s worth noting that the formation of new Cherokee identities was ongoing far after the colonial era. The Cherokee Nation and Eastern Band of Cherokee Indians retain strong bonds of kinship and culture, but because of removal and their separate locations, have had distinct experiences for nearly 2 centuries now. This is manifested in their unique identities in terms of dialects, oral traditions, even cultural values, etc. And the Eastern Cherokees incorporated some Catawbas into their kinship networks in the post-removal era, which has affected their pottery traditions, to name one impact.