'To know' might be a difficult thing to pin down with concrete examples.

Firstly, I gather your question might be very specific to the 1492-1607 timeframe, I'll still try to expand your question into several different ways of interpreting it, roughly following following the four main periods in time that native Americans and the Old World might've had prior contact, that migh've brought with them some knowledge of the Old World.

Secondly, I am by no means an expert in any of the fields related to native Amerians, tribes and culture and history. Therefore a real expert should try to dig into the post-Columbus indigenous cultural exchange within the native population.

a) To start off with the trivial answer, due to the initial migration of natives into america over the siberia-alaska land bridge happening so many tens of thousands years ago, there is likely no remnants of anything one could consider a common culture with the other homo sapiens groups that ended up in western europe.

b) a very hypothetical link of sea-farers from ancient Egipt crossing the Atlantic and reaching the Caribbean, briging with them some cultural elements. This is something proposed and demonstrated by the Norwegian etnographer Thor Heyerdahl in his Ra expeditions. Any possible connotations from it however are largely anecdotal at best and opposed by the majority of field experts. Even so, any knowledge the natives might've gotten from a single expedition like this would likely devolve into a myth about a minor deity over the next thousand years, so likely no real geographic knowledge, if even that.

c) Moving northward, the Leif Ericsson expeditions to Vinland/Newfoundland area. The contact was again very brief (only a few years) and more hostile natured than a peaceful culture and trade goods exchange, so any meaningful info was likely contained within the handful of people into whos lands the vikings settled, and was likely forgotten soon thereafter (within a few generations) as an unexplained historical curiosity, maybe a 'made-up grandpa-story', if even that.

d) Moving back down, the first explorers from the post-Columbus area and first settlements on the current US mainland.

Spanish colonists and explorers, who would likely be the sole option for pre-British contact and information spreading, focused a lot on the islands (first main colonies and power-base) as well as south and central America, so it would he difficult to imagine word of mouth travelling all the way from today's Belize to Virginia on land, due to there no being a real road infrastructure and the areas often separated by natural barriers, thick forest, swamps, rivers, mountains, dry wastes, etc.

The first settlements of Spain in the mainland US from 1513 onwards failed. The main focus seemed to be on Florida. In 1562 some French outcasts found their way to the uncolonised north Florida coast. This annoyed the Spanish, so they wiped the settlement out in 1565 and put their own fort there in St. Augustine, which became the first real, albeit minor foothold in the mainland. Further colonisation attempts north of Mexico took the rest of the century to happen, but that is already very close to the British arrival and those attempts were also pretty modest at first.

So I recon the real exact question to pose is - "How much did the Spanish explorers interact (friendly or hostile) and trade with the indigenous peoples living north of the Florida coastline, all the way up to Canada?"

Any expert comment here is very welcome.

If there was anything besides small bands of spanish explorers killed or driven out of an area then we might consider that some form of umderstanding of other cultures, continents and countries and peoples started entering into the worldview of the natives from the middle of the 16th century onwards.

However, keep in mind firstly that information spread at that time was very, very slow, especially between different tribes, migratory or not, nad who might've been hostile to each other.

I would not consider it a likely possibility that information like that (Spain as country and Europe, etc) spread as the word of mouth even from Florida to Virginia within the half-century.

Poentially I can see informatio that 'new hostile pale-skin tribe with big ships are attacking in the lands to the south' travelling so far, but little more. But being so distant, maybe discarded as a curiosity again.

Secondly, keep in mind that the notions we're so accustomed to - country, kindgom, vassal, nationality, Army, Navy, etc - are likely very much a part of the European culture sphere at the time. Don't get me wrong, similar words and similar themes were definitely in use elsewhere, Middle-East, China, India, sub-Saharan Africa, etc, and these could more easy be translated from one language to another and placed in the socio-cultural framework of the listener to make sense. What I don't have an answer to is whether the Native American tribes also even had a framework to make a lot of sense of the 'new pale-skin man' world, which would've helped it to spread more quickly, since everyone would understand.

Any expert comment here is very welcome.

(E.g. we understand perfecty if King A attacks King B to claim territory, a Dukedom belonging to Duke C, a Vassal of King A. But if we used unknown/untranslatable terms or a hierachical/social/cultural framework we're not used to, it might be very difficult to understand the heck is going on. And who to root for. And how to pass this information on to our friends.)