Not all that far-fetched. Many tribes had been decimated by diseases and warfare. They actively sought to add people to their tribe. My 2x great grandfather was actually adopted by the Sioux.
I grew up in an area of SC close to the NC border where Native Americans, mostly Lumbee, also lived. When I was growing up, it was very common to hear people referred to as a “Croatan” meaning they had mixed Indian/European ancestry. You would often see someone who’s family was Native American but they would stand out because they had blue eyes. It was common lore in that area the lost colonists weren’t lost- they just went to live with the local tribe and had hoped the letters they wrote would tell anyone else where they had gone.
My 7x great grandmother was captured and enslaved by the Comanche and went in to be one of the early settlers of St Louis. She has her own Wikipedia page!
https://en.m.wikipedia.org/wiki/Maria_Rosa_Villalpando
And my 6x great-grandmother was adopted by the Mohawk.
Guns & Cannonballs, naturally occurring. Hammerscale, proof that the English were there.