I tried your search. On the first page of hits, there was just one that mentioned "final solution," and that was from 1910:

“It is readily acknowledged that Indian children lose their natural resistance to illness by habitating so closely in these schools, and that they die at a much higher rate than in their villages. But this alone does not justify a change in the policy of this Department, which is being geared towards the final solution of our Indian Problem." [1]

[1] Department of Indian Affairs Superintendent D.C. Scott to B.C. Indian Agent-General Major D. McKay, DIA Archives, RG 1-Series 12 April 1910

The quote is from the Canadian poet and Indian Affairs bureaucrat Duncan Campbell Scott, who wanted to solve Canada's "Indian Problem" through active assimilation and elimination of the Indians' separate ethnic identities. This was to be done by forced government schooling, which, as the quote acknowledges, carried a fairly brutal death rate for the children who were forced to attend. The point was not to kill them so much as to make them regular, English-thinking Canadian citizens, who would not then require separate arrangements with the Canadian government.

I don't know if the term "final solution" used here is related to the German use (Nazis or Herzl) or not. The time frame is similar, but it is also a different language and cultural/political salient. I believe the German term is 'Endloesung'. In either case, it is obviously a complementary trope to "X Problem" in reference to a problematic minority, and the two cases might have been coined independently.