Arguably the first contact between the Old World and the New World occurred around 3,000 BCE when the Eskimo peoples began crossing the fifty miles of the Bering Strait to Alaska. Originally a people of the Arctic Coast of eastern Siberia, the Eskimos were well adapted to the freezing North American shores of the Arctic Ocean, which was a good thing given that the more habitable territories of the New World were already claimed and the Eskimos lacked the numbers needed to displace them. The Eskimos brought with them several innovations unknown to the earlier Amerind and Na-Dene migrants, notably the bow and arrow, which even after spreading across Alaska and northern Canada did not spread south for some three thousand years for god only knows what reason. Anyways, unlike their predecessors, the Eskimos continued to have fairly regular contact with their forbearers back in Siberia, including conducting trade and some groups moving back and forth between the two land masses. This likely continued to at least 500 CE, with many pieces of Old World technology, such as the crossbow, making its way to the Eskimos. Most likely, semi-regular contact between groups in Alaska and western Siberia never ceased. However, given the isolation of the groups in both Siberia and the North American Arctic, such exchanges had little effect on the rest of the New World.
The first definitive contact between Europeans and the New World took place some four thousand years later in 1000 CE. At the time, the Norse of Scandinavia were a expansionist people, sailing their well crafted long ships long distances, including west to the British Isles, south to the Mediterranean Sea, and east deep into the heart of Russia via its many rivers. In 870 CE, a group of Norse, blown off course while sailing to the Faroe Islands, discovered Iceland, home to only a few scattered communities of Irish monks. At the time, such monks had made their way to many isolated islands, both looking to spread the word of the Christian god and to find places of peace from the near constant Norse raids in Ireland. By 930 CE, the entirety of Iceland’s habitable lands were settled. In 980 CE, a Norseman by the name of Erik the Red was banished from Iceland for manslaughter. Unable to return to Norway for similar reasons, he took a gamble based on rumors of land masses further west, discovering Greenland after sailing some 700 miles. Erik sent word to Iceland for more settlers to follow, and eventually some 3,000 Norse called Greenland home. In 989 CE, a group of these settlers, led by Bjarni Herjolfsson, was blown off course sailing to Greenland. Finding themselves far to the west, they spotted land but decided to instead push on to Greenland. This was the first verified sighting of the North American coast by a European.
Erik the Red’s son, Leif Erikson, was enraptured with the idea of discovering a new land like his father. In 1000 CE, at the age of thirty, he got his father’s blessing to proceed and sailed west. After crossing some 650 miles of open ocean, he arrived in what is today Labrador, before moving south to present day Newfoundland where he camped during the winter before returning home. Calling the new land Vinland, Leif told the Norse of Greenland about a wonderous land full of giant trees and strange native peoples he called Skraelings. Enticed by the promise of large trees, something decidedly lacking in Greenland, Leif’s younger brother, Thorvald Erikson followed his brothers route westward in 1004 CE, camping for the winter in the same spot. However, unfortunately Thorvald was killed by the Skraeling, who attacked in retaliation for an earlier unprovoked attack by the Norsemen. His fellows took his body back to Greenland. This slowed thoughts of returning to Vinland, at least until 1009 CE, when Thorfin Karlsefni decided to found a new settlement in the mysterious land. Leading some 200 women and children, he set sail and did just that, but had little more luck than his predecessors. Though at first peaceful trade was established with the Skraeling, a misunderstanding quickly led to violence, and the settlement was abandoned the next year. After that the Norse largely gave up on the idea of Vinland, though a few expeditions did come westward over the years to cut lumber, hunt, and do some trading. However, this ceased as the Little Ice Age began, which eventually forced the abandonment of the Greenland settlements in 1350 CE.
Another point of contact between the Old World and the New World was likely the Polynesians. Expert sailors, the Polynesians took their outriggers thousands of miles across the Pacific Ocean, discovering and inhabiting island across the southern hemisphere. These settling sailors reached Easter Island and the Hawaiian Islands around 400 CE. While no written records exist, it is possible that the Polynesians of Easter Island crossed the 2,300 miles of open ocean to the west coast of South America as early as 700 CE. At least it was around this time that the sweet potato, indigenous to South America, mysteriously spread westward across Polynesia as a food crop. A more definitive period of contact took place between 1300 and 1400 CE, with Polynesian genetics appearing amongst some Native American groups, indicating some level of settlement and intermingling.
Beyond the largely confirmed Siberian, Norse, and Polynesian contacts, numerous other legends and rumors claimed early contact by Romans, Irish, Welsh, Chinese, and Japanese. However, no proof exists that any of these contact ever actually took place. Is it possible that isolated incidents did occur. For example, during the 17th through 19th centuries several dozen incidents took place where Japanese sailors cast adrift in their damaged vessels arrived at the Pacific Coast of North America at times over a year later. However, even if they did occur, such contacts would’ve been little more than curiosities, with no actual meaningful impact on either the Old World or the New World.