Well, one posibility is to have a group of
Yaghans get lost because of a storm near Isla de los Estados. IIRC, currents might take them to the islands. Yagahns traveled with their families, so, if you could enough cannoes toghether and have most of them arriving to Malvinas, I guess they could have survived and given rise to a local population. If their cannoes are damaged, they might be force to remain there, as there aren't any trees in Malvinas. They would have to abandon their way of life an become land-based hunters or fishmen.
I know, this scenario requires a lot of "coincidenses": having a group of Yaghans togheter near Isla de los Estados; their being derailed to the Islands (a pretty long distance); the destruction of their canoes; their survival to the wreckage and their giving rise to a native people. It might still have been possible, but it's not the most likely one.
Another possibility would be to have humans crossing walking at a time when the sea levels were lower. But I'm not sure if sea levels were once low enough to allow humans to cross.
Yet, even if both scenarios seem quite unlikely, it's a fact that canids managed to get there somehow, as Seluco VII said. And quite a few argue that these arrived to the islands
with humans, who
had to come there in one of the ways stated above (or in a variant of those, i.e., by sea or by land).