Right from the beginning, the xenarthrans--armadillos, sloths and anteaters--have been at a disadvantage. For the longest time, their home was an island continent, which made them extremely vulnerable to outside environmental changes. Case in point--the American Interchange caused by the bridging of Panama less than three million years ago. As quoted in Wikipedia:
During the Cenozoic, North America was periodically connected to Eurasia via Beringia, allowing repeated migrations back and forth to unite the faunas of the two continents.[n 21] Eurasia was connected in turn to Africa, which contributed further to the species that made their way to North America.[n 22] South America, on the other hand, was connected only to Antarctica and Australia, two much smaller and less hospitable continents, and only in the early Cenozoic. Moreover, this land connection does not seem to have carried much traffic (apparently no mammals other than marsupials and perhaps a few monotremes ever migrated by this route), particularly in the direction of South America. This means that Northern Hemisphere species arose over a land area roughly six times greater than was available to South American species. North American species were thus products of a larger and more competitive arena,[n 23] where evolution would have proceeded more rapidly. They tended to be more efficient and brainier,[n 24][n 25] generally able to outrun and outwit their South American counterparts, who were products of an evolutionary backwater. These advantages can be clearly seen in the cases of ungulates and their predators, where South American forms were replaced wholesale by the invaders.
Unfortunate in the long term, so how could we toughen them up? Why, give them more space to roam at a far earlier date. (Could put them in ecological crossfire with the rodents and eulipotyphlans, but that's not relevant to the question here.) Fortunately, we have an idea on which directions some particular ocean currents took during the Eocene:
The current was very close to South America at the time, and if we look really closely, we can see that the Panamanian Land Bridge had just started to emerge. Now the question is: Could that current ferry the armadillos and sloths outside of South America to colonize other lands long before the Great American Interchange?