Is there a particular reason you are enquiring about the year 1414 AD? Does it have a particular significance? I don't believe it has a particular significance in Hawaiian history, as we don't have any written record of the Hawaiian language before approx. 1830 AD. Polynesian languages in general, and Hawaiian in particular, were purely oral languages for the vast majority of their histories. Christian missionaries assisted in creation of an alphabet for Hawaiian in 1826, in pursuit of a way to compose the Bible into Hawaiian, and the first complete Hawaiian grammar book (Über die Hawaiische Sprache) was published in Berlin in 1837.

That being the case, we have no written histories to refer to in our study of Hawaiian history. We must instead use a combination of oral histories and comparative linguistics to make educated guesses about the origins of the original settlers of Hawaii, and their knowledge of the wider world.

Using lexiostatistics, language experts are able to use several hundred words that are common to any language (blood, water, 1-10, hair) , and compare them to the same small vocabulary of words in another language. By doing so they are looking for cognates, identical sounds, similar sounds, or dissimilar sounds. Languages that are extremely similar, with many cognates and similar sounds for the same words, can be reasonably determined to be related. For instance, English and Hawaiian share 0 cognates or similar sounding words for the same 200 concepts, while Tahitian and Hawaiian share 152 cognates or similar sounding words out of 200. They are also able to use the drift of sounds in common words to determine how lately one language has split off from another, to give an idea of how long two communities with similar languages have been separated.

Using this lexiostatistic theory on Hawaiian, we have been able to determine that Hawaii was likely settled at the latest by 800 AD, although it is possible there were people on the islands as early as 300 AD. They likely came from the Southern Marquesas, a chain of islands in French Polynesia about 4,000 kilometers to the SE of Hawaii (see map here. These initial settlers would have brought with them the classic Polynesian agricultural system of taro, banana, breadfruit, sugarcane, chickens, pigs, and dogs.

There is some evidence that there was an invasion of Hawaii in approx. 1300 AD by an expedition or migration from Tahiti, but this is contentious. Some experts subscribe to the theory of Tahitian conquest in one large migration, whereas others argue for a more gradual exchange between the two cultures, with a series of small migrations between the two island groups.

The invasion theory is partially supported by two Hawaiian oral legends, that of Hawaiiloa and Pa'ao. In one, after discovering the island by accident, the great hero Hawaiiloa travels from Kahiki (Tahiti) with his family and several other navigators to found a new settlement on the big island of Hawaii. In the other, Pa'ao, a priest and navigator, comes to Hawaii from Kahiki ; which in this case is understood to be either Tahiti or Samoa. I believe that for Hawaiians, Kahiki eventually came to be a term that encompassed any land that was not Hawaii. Pa'ao was said to have come to Hawaii during the reign of one of it's legendary kings, but eventually this line of kings became corrupted and degenerate. Pa'ao thus went back to Kahiki to fetch a "pure" king, who then came to rule over Hawaii. This king was then looked to as the progenitor of the Hawaiian royal line, particularly that of King Kalakaua. Of course, any such oral history has to be taken with a grain of salt.

However, all sources agree that there was some limited contact between Hawaii and several islands in French Polynesia between approx. 800 AD and 1300 AD; likely consisting of a mix of small migrations, military campaigns, and trade missions. These voyages seem to have dropped off after approx. 1300 AD, for unknown reasons. By 1778, when Captain Cook made the first European contact with Hawaii, the original settlement and possible later conquest of Hawaii had long passed into myth. In 1414, we would only be approx. one century removed from the latest migration from Tahiti to Hawaii (setting aside if it was a conquest or not). So it is possible that Hawaiians living in this era would have had some knowledge of Tahiti, and the chain of islands far to the south from whence these settlers came. This is not to say however, that they would have any conception of the vast landmasses and completely different geographies and cultures of North and South America, Asia, or even Australia. I believe it would be safe to say that in 1414 Hawaiians would not have been aware of the existence of the Asian or American continents.

As some had said there is no written Polynesian language to confirm. Though the Polynesians of Rapa Nui (Easter island) had a hieroglyphic version that was destroyed by Jesuit priest when the Spanish came. Only five tablets survived and the writing is has been unable to be translated. That said however.

You will find in the Hawaiian langue spelled differently, and many words pronounced differently than Tahitian, or Rapa Nui, or Aotearoa (New Zealand) of that Polynesian group. They can still understand what they are saying to each other as weird as it may seem. However regarding Micronesian or Melanesian they cannot understand the language of each other. You would think that, but that does not happen. Probably as some surmise each group of Polynesians from different lengths of sailing history and place of origins. "Polynesian" is not even an appropriate word to describe each group IMO. The term "Polynesia" was first used in 1756 by French writer Charles de Brosses, and became an accepted anthropological term to describe the people of the Pacific. Such broad wording can confuse the novice not familiar with each islands origins, and tend to lump them all together. That is like saying all Britons are the same people. Whereas Britain was made up of many tribal ethnic groups from different parts of Europe. Such as Danes, Saxons or Romans, or Celts etc...

Hawaiians kept history through a system handed by chants passed down through what we call Kumu's (teachers). Think of these as the equivalent of Viking Sagas which also described America and founded Iceland, Greenland and a part of North America. These were told around campfires or dances such as you see in Hulas when the song is sung in a chant etc...

There are many stories ranging in mythology, folklore, and also in principle in teaching. Such as how to build a voyaging canoe or growing calendars to remember by so you can fish certain species by moonlight or when it was kapu (forbidden) to catch for propagation reasons of the species like lobster. Also for genealogical history of their ancestors.

In such chants. There are tales of two Polynesians coming from the land of Uru. Uru was considered the land east of Hawaii. Hatu Matoa was the first who supposedly sailed from Uru estimated 250 BCE to Rapa Nui and founded the civilization on Easter island. Hawaii Loa sailed first from Uru estimated 50 BCE in Hawaiian calendar north up the coast to California, and stayed, and resupplied for several years there. Then set out and landed in Hawaii.

This is only supported by Hawaiian families that trace their clans through such kumu chants and recorded their genealogy all down to Hawaii Loa, and others in Tahiti and Rapa Nui to Hatu Matoa (whose ancestors supposedly pushed out from Rapa Nui, and settled Tahiti, and later on Aotearoa).

That is on the verbal end of history. Now a concerning archaeological history. There is only archaeoligical evidence pointing earliest of Hawaii founded in 700 CE, so 50 BCE may seem a reach on the verbal end. However many Hawaiian sites were destroyed by construction for building and golf courses. One developer just piled the bones up and had them grind for gravel. Crying shame really. However more modern laws prevent such exploring, and discovering a site must be done in accordance with Hawaiian policy like Native Americans have now for their sacred sites, so research is limited now. However he fact the the genes in the sweet potato and kalo come from South America in origin, and recent finds of the Polynesian Chicken, and Polynesian bones in the islands off Western Chile (Uru?). It would seem to provide enough proof that Polynesians did come, and be aware of South America. Also based on their knowledge of the Ku Holo (ancient art of navigation without a compass) via voyaging canoes, and through Captain Cooks translators teaching them to navigate pacific currents to find Hawaii. There was much sailing among Hawaiians and other Polynesians to know about Asia and The Americas.

BTW they find canoes from coastal Indians of South America that use the same planking method as Polynesians, and use the same design of integrated weaving the board together, and method of carving fishing equipment out of bones as another example. Some might say that is coincidence, but the fact is Polynesians have been sailing the Pacific for centuries long before Christ. That can no longer be disputed as such has been scientifically replicated of the old method of building such canoes from scratch, and using the same navigation techniques handed down through kumu's via chants, and is now accepted by academia.

Now would they have knowledge of Americas and Asia before 1414? What do you think now?

Also FYI if questioning my knowledge comes from my kumu Chadd Paishon. Who is Pwo (master navigator of the ancient Ku Holo) of the Makali'i voyaging canoe, and accepted by academia in Hawaiian sailing history and its ancient navigation. Also I do have a education in Hawaiian studies.