This kind of work has already been done with the languages of Europe and other parts of the world. That’s how we know that Spanish, Greek, Hindi, English, Irish, Russian and Armenian are all part of one language family and probably had some common ancestors. Things aren’t so clear when it comes to the Americas, but it’s as good a guess as any.
And very little more than a guess.
There may be better source material in John Peabody Harrington's notes than one might suppose. California had at one time the most diverse language geography in North America, with seven major language groups which Harrington documented meticulously. He never bothered publishing anything, instead focusing upon capturing all that could be done. Linguists to this day are surveying his over one million pages of notes.