Could dinosaurs have been discovered on the Americas during the age of discovery?
Some things to take into account:
So would it be possible for these animals to have been completely unknown to Europeans up until they landed there?
Assuming you mean "Could dinosaurs that went extinct in Europe at the same time as dinosaurs went extinct in the real world but survived in the Americas be completely unknown to explorers of the New World, even though there are the same species?" then the answer is definitely yes. The first dinosaur fossils ever recognised were found in either the late 1700s or early 1800s depending which specimen you look at; Colonisation of the Americas began in the 1490s. So Europeans seeing dinosaurs in the Americas would have no fossil references of their Old World equivalents.
Yes... and it's obvious
When the first European explorers stepped foot anywhere in the Americas, their very first experience would be to see a native running toward them with a Velociraptor on his tail screaming hualmotlaloa amonemiliz!1 Not that any of the Europeans would have understood it, though they might have gotten the gist when the Velociraptor started eating the crew.
If you'll forgive me, this question seems a bit trivial. Dinosaurs are big and somewhat inimical to humanity. How could the Europeans not find them?
However, if you're actually asking how the eastern hemisphere would be devoid of dinos if the western hemisphere did. I consider that impossible without moving where the meteor hit (i.e., it hit in Europe but only caused a hemisphere-wide extinction. However, that means no land bridges during all those millions of years, which is also really hard to believe. So, methinks you're in for some serious handwaving.
1 "Run for your life!" more or less in ancient Nahuatl.
Sort of...
So, first off, you nee to have the dinosaurs go extinct in Africa, Asia, Europe, and North America as usual, but survive in South America. In the Cretaceous period, North and South America were not connected by the isthmus of Panama -- they would not connect until around 2.7 million years ago during the Great American Interchange.
Next, you need to make sure that dinosaurs don't make it to Asia during the last ice age. This is the point where humans made it to the Americas, some 20-40,000 years ago, when lowered sea levels created a land bridge between modern Alaska and Russia. This shouldn't be too hard, since all of modern Canada and parts of the norther United States were covered in glaciers. Just make sure that the dinosaurs do not adapt to the cold too much and keep them closer to modern Mexico until the glaciers recede and the land bridge disappears.
The reason I say "sort of" is that since the dinosaurs died off, humans and all other mammals evolved from small rat-like animals. There are species, alligators are a good example, that have not changed their appearance very much since the Cretaceous, so I think you could make some plausible arguments, you just need to think about how dinosaurs evolved enough to survive extinction while still maintaining the size and appearance you want, and also think about what ecological niches they would fill to survive alongside all of the new mammal species first in South America for about 20 million years and then alongside a new host of North American mammals for another 3 million years before finally meeting humans.
In the real world, dinosaurs went extinct about 66 million years ago. Not just one species of dinosaurs went extinct, all of them did (except for the birds).
So would the dinosaurs not go extinct in the Americas, and only there, and stay there until the Age of Exploration? What stopped them from migrating elsewhere back when the continental plates were linked differently?
To explain surviving dinosaurs in North and South America, but not in Europe, the best story is that they ranged worldwide until after the last ice age and the end of the Bering land bridge. Then they went extinct in Europe, Asia, and Africa, but not elsewhere. How to explain that? A dinosaur-specific plague?
That might bring fuzzy folk tales of "terrible lizards" prompted by the much more plentiful bone finds.
Given that some dinosaurs* survived the extinction event, it's certainly plausible that they might be limited to a few continents. In fact, there's a somewhat parallel example, the marsupials: https://en.wikipedia.org/wiki/Marsupial#Evolution They diverged from placental mammals long before Chicxulub, yet they are found primarily in Australia & adjacent islands, and in South America. (With one species, the opossum, in North America.) Likewise, there are few placental mammals native to Australia.
There are two factors you'll have to account for. First, what happened to the marine reptiles? (Not strictly dinosaurs, but popularly thought of as such.) Either the extinction event wiped them out, or they should be everywhere in the oceans. Second, remember that the dinosaurs have had ~65 million years to keep evolving, so they're not likely to be the same as what was around immmediately pre-extinction.
*Birds diverged from dinosaurs long before.
The real question is: What would have prevented the natives from eating all the dinosaurs?
Most of native fauna disappeared when humans came to America. There were lots of interesting species of large mammals in the Americas. They all disappeared more or less around the time first humans arrived. Probably ended up as steaks. Except for the tougher bits, which became stew.
You need to explain why humans did hunt mammoths into extinction, but not large dinosaurs which were slower and dumber.
