The earliest American history is that of the Native Americans or pre-Colonial. Then Columbus and the Spanish explorers, then early colonies of the English, Dutch... Of course, there's a possibility that many others made it to our shores through migration, exploration, and ship wrecks.
I thought this video by the World History Channel was well made and interesting...
The Pilgrims were religious Christians who were in conflict with the Protestant Church of England. They fled due to religious prosecution. King James gave permission for them to establish a colony in Virginia and Virginia was a great expanse at the time including parts of what is Pennsylvania and North Carolina today. William Bradford, one of those passengers on the ship named the Mayflower, left a journal and so we know a lot about their voyage... They departed weeks late and their provision ship, the Speedwell, leaked so they went on without it. They bravely went to an unknown country, going onshore far from their original notions of a destination and faced a harsh winter climate. They had not landed in Virginia at all.