They could just try to take it over the same way they took over the United States. Find some true believers or buy off people to put in positions of authority. Use them to disregard norms and traditions and look for loopholes to change laws. Flood the country with disinformation. Hell, maybe Elon could give everybody a million bucks to sign a petition. Soon enough, Greenland is pro-USA all the way.
I don’t know how well these tactics would work in such a small population. But who knows?