On a smaller scale, I believe this has happened; I recall reading about a botanist that noticed certain fruit plants were found in long trails, and showed that these trails corresponded to ancient "circuits" of hunter-gatherers, that probably gathered and carried the food plants with them to eat along the way, and pooped out the seeds along the trail.
One might see a similar thing in the fossil record. A concentration of many fossils in a particular area of origin, that are exclusive to a time period before say 5000 BC, followed by a growing diaspora of scattered fossils after that period.
We can tell by various means when fossils were laid down, when animals migrated, etc. Even delicate plants fossilize, we have many fern fossils from tens of millions of years ago.
That would indicate unnatural transportation. I mean, squash a zoo (somehow), fossilize the animals, and it is hard to devise a non-intentional explanation for why so many different animals that originated all over the world happen to be in the same place in well ordered and distinct locations, in such small numbers (a handful each of tigers, giraffes, hippos, elephants, seals, etc.)
Eventually the hypothesis would have to be artificial transportation of the species. The key here (as you seem to intuit) is time and fossil dating: A concentration of something for many millennia, followed by a near instantaneous spread, but in very thin numbers, to other continents and places, such that it is nearly impossible for that to be a natural migration; the only plausible explanation is an assisted migration, which means an intelligent entity capable of transporting the animals (or plants) long distances is responsible.