The problem is discovering how far back? In the days of Sail it took about a week to go from the East Coast of what is now the US to get to Europe, but Six weeks the other direction. This was the chief limitation on contact.
During the middle Ages "St Brendan's Land" was often marked on European maps showing something was here. Exactly what was unknown but legend of St Brendan's land was while known (even the Viking report finding Irish Monks on some of their Explorations of what is now North America). This is the easiest reliable reports of people reaching America.
Then came the Vikings, who disappeared from North America during Black Death but quickly replaced by various Fishing boats from various fishing communities of Western Europe during the Centuries between the Vikings and Columbus. Officially the fisherman never set foot on land, but I just do NOT see them doing that given the location of the Great banks (Which is where they were fishing) and North American. Furthermore in 1497 John Cabot sailed from England to New Found-land and claimed it for England (and Spanish maps of the early 1500s calls that Area the "English Seas" (England and Spain had been Allies against the French for almost 200 years at that point of History, but not so friendly as for England to abandoned its Fishing Fleets to the mercies of the Spanish).
For more on St Brendan's land:
http://www.irishcultureandcustoms.com/ASaints/BrendanNav.htmlhttp://www.castletown.com/brendan.htmhttp://www.seiyaku.com/customs/crosses/brendan.htmlNow they are some records of even earlier European contact with North America but these are considered NOT trustworthy by most Historians (i.e. do NOT match up with travel times or geography that is known, even S Brendan's story has problems with it, to many "40 days" sailing durations but it does match up nicely with a trip from Ireland to Iceland to Greenland to New Found-land and we have the Vikings stories of finding Irish Priest everywhere they traveled).
Now some confirmation of earlier travelers can be the product of contamination. The classic case is London mud. During the Roman ear of London, a Bridge existed where London Bridge is today. People would lose coins over the side of said bridge for it was a major port area. During the Colonial era this same area was again a port for London. In this period large barrels of Mud was drawn from the Thames to be used as ballast on the trip right is now the US East Coast. These ships would work they way up various Us East Coast rivers selling their London Products, finally getting to the "Fall Line (a line where ships could no longer travel up stream) sell they remaining products, buy tobacco or later Cotton and dump the Mud into the river. The goods from England were light in weight compare to the Tobacco going from the East Coast to London, thus in London the ships needed to ass weight, in America as they traveled up stream they had to lose weight. Thus the barrels of Mud were dumped.
The significance of this London mud was it sometimes contained Roman Coins from the Roman era. As the mud was loaded onto the ships no one looked at what was in the mud, all the Captain wanted was WEIGHT, thus the mud with the coins traveled to America and dumped in Various American Rivers of the American South. Occasional these are found and presented as "Proof" the the Romans's were in North America, when it fact all they are are indications of contamination of one Archaeological site (The US) with the archeology evidence form anther (London in this example). No evidence of Roman visitation to North America has ever surfaced (Other then what is better explained as contamination) nor do we have any ROMAN records of Explorations (The Romans were notorious for NOT exploring, Nero might send two Centurions to find out the source of the Nile, but none to find out the coastline of Norway and Sweden or even Britain). The earlier Greeks (and later Dark age Christians) did more explorations than did the Romans. Basically if the Romans could NOT make money on something they care less about it, thus it is unlikely any Romans came to North America (The Romans till late during the Empire seems not even to be interested in Ireland or even Scotland, they knew of both but that is all).
Similar Stories are Said about the Greek, the Phoenicians, Ancient Egyptians (and even Chinese, through that is more directed to the West Coast of the US and apparently only AFTER Columbus, but within 100 years of Columbus Discovery of America). None of these stories do appear to have any support.
Some historians support these stories early "finders" of North America, they rely on guess work to fill in weaknesses in this line of sorties. For example I read a paper where one historian says he could not find enough Copper in the Mediterranean to supply all the Copper and Bronze used in the late Bronze age. He could NOT determine where all the Copper from the Copper Mines of Michigan mined roughly during the same time period went to. This period is also the period where huge boulders were put up at various places in the North Atlantic, these boulders were used as navigation guides till this very day. Viking report using them as navigation aides but claim they did NOT know who put them up, no one knows who put them up. This period (about 1000BC) is also a period of hugh canoe building by fishermen off the East Coast (through NO findings of any Canoes with copper, as opposed to Copper items, in the canoes from the same time period) . One can connect the dots and see a huge trade in Copper from Michigan to Greece that was disrupted by the switch over to the Iron Age (and never renewed) but whatever happened in lost to history and even the historian who tried to connect the above facts point out they is NOT enough facts to call his idea any thing more then speculation. His observation of lack of Copper in the Mediterranean may just be his failure to consider how extensive the mining of Copper of Cyprus and England had been during that time period (and destroyed by subsequent Copper Mining during the Iron age). His observation of not enough Copper items form the Copper mines of Michigan may just be that the copper was buried in Graves we have NOT found (Indians in the Historian period tended NOT to bury their dead, that was NOT always the case).
Ancient Copper mining in North America:
http://www.ramtops.co.uk/copper.htmlhttp://www.unr.edu/sb204/geology/coptext.htmlAs to the Native Americans, even after Cortez they were the majority of people in Mexico (and remain so to this day). Small pox killed a lot of Indians off (as Small pox also killed off a lot of Whites), in North America the Native Population never made the needed adjustments to be able to fight off the Europeans (and those that did apparently joined the "White" society during the 1600s and 1700s, we have huge number of stories of Indians living among the whites during the Colonial Period, they became the poor of Colonial Society and slowly "disappeared" as the Indians were driven westward across the Mississippi. A lot of Americans whose families were here before the Revolution have a lot of native blood in them, most never admitted do to the hatred of Indians caused by the Conflict between whites and Indians).
My point here is that the Spanish hold on early American History was weak, it was like a light spring wind, felt but then forgotten (Like all of the previous European contact with North America). It is only with the White settlement of North American that the biggest influence on this Continent shifted from the Native Americans to white Society And even that was weak, for a good bit of our farming techniques, especially north of the Mason-Dixon line, is a combination of German and Indian farming techniques. Thus it would be better to say that the Growing Mexican population in the US is more a product of Native Americans increasing their influence then of Spanish Americans.