But being a little more practical for genealogical research, the first arrivals began with Columbus in 1492. Spain, Mexico and Peru have some of the oldest and most complete genealogically valuable records in both Europe and in North and South America. See "Hispanic Family History: Research in the Best Records in the World" by George Ryskamp on Ancestry.com. By the time English speaking settlers arrives on the East Coast, in the early 1600s, Spanish language records had been kept in Peru and Mexico for almost 100 years. Quoting from George Ryskamp's article concerning records in Spain:
A brief survey of the Guía de la Iglesia en España (Oficina de Estadística: Madrid, 1954), which lists more than 90 percent of the parishes of Spain, offers proof of the antiquity of record keeping in the Spanish parish. The oldest known parish records are found in Solsona, Spain and date from the year 1394. At least 37 parishes have records before 1500. Nearly one-third antedate the year 1600, and nearly one-half antedate the year 1650. As early as the end of the 15th century, Cardinal Cisneros, in the first synod of Alcala, ordered that records of baptisms, marriages, and deaths be kept throughout Castile.Latin American parish records (at least of baptisms and marriages) were kept with equal faithfulness. When the Americas were colonized, Spanish record systems were immediately transferred to the New World, where the earliest records in Lima, Peru begin in the year 1537.In some cases, using Catholic Church records, you can trace Latin American ancestors back into the 1500s. I mentioned Native American records, on the East Coast of North America, some of these records date back to as early as 1774. See Researching American Indians and Alaska Natives from the U.S. National Archives. See also NativeWeb.org Resource Database / Genealogy (Tracing Roots) / American Indian and First Nations Genealogy
Those who emigrated from England to the American colonies began keeping records almost immediately. One of the earliest collection of records is that of the Jamestown Records of the Virginia Company of London dating from 1553 when the Company was organized. See Virginia Records Timeline from the Library of Congress.
Once you trace your ancestry back to an immigrant, if you can identify the immigrant's place of origin, you will then need to pursue your research in the country of origin.