The last time I asked something similar, I asked if it would be possible for xenarthran mammals (armadillos, sloths and anteaters) to be thrown off of South America from life-giving rafts to other parts of the world. The possibility is very strong that they could survive the long treks across oceans. So the odds of armadillos and sloths colonizing other continents outside South America within the Paleocene-Eocene window are high.
But what of perhaps the most charismatic of South American mammals, the meridiungulates? If you've never heard of them, don't be disappointed. This clade died out during the Younger Dryas climate chaos 11,000 years ago. The meridiungulates were a group of hoofed mammals that were sister to the perissodactyls (horses, rhinos and tapirs) but were strictly original to the island continent of South America, which no longer became an island when Panama connected North to South as recently as the late Pliocene epoch some three million years ago. They ruled South America from the Paleocene all the way to the Pleistocene, their reign undone by a combination of climate change and competition from northern hemisphere ungulates.
But what makes the meridiungulates particularly interesting is that not all of them lived their lives like the other hoofed mammals. Some of them were small enough to look and act like rabbits!
So within the Paleocene-Eocene window (59-36 million years ago), would it be possible for some of those small, rabbit-like meridiungulates to get rafted out of South America and eventually land on other parts of the world (preferably North America, Africa or both)?