The USA is a complex, multifaceted and huge nation. Nailing down a particular early settlement as America's cultural birth is difficult, because modern America is realistically, a fusion and mishmash of various cultures, trends and events.

Early American settlements might have laid some of the foundations, but realistically, modern America is a product of the years between now and then. The Revolution, the Civil War, the waves of immigration,etc all changed American society fundamentally. Colonial America would have been foreign to an American in the 1870s.

Many of the early settlements, not just Jamestown and Plymouth, were relatively isolated from each other and had different approaches to economic, political, religious and social issues. In some respects they could be foreign to one another. A settlement like Plymouth, settled by the Pilgrims, was worlds apart in religious and social dynamics from Old Baltimore, settled by English Catholics, to make matters more distinct - they were also far apart from each other geographically. It wasn't until the 1700s that overland travel between all the continental North American colonies became both convenient and regular.

Even further, the settlements in British North America during the 1600s rarely, if ever, acted in political concert or coordination. They prosecuted wars and treaties separately, they had different responses to events back in England, they had different economies and trades, they were populated by different people. Whilst some regions, like New England, certainly developed a shared identity, it would take a while for a shared American identity to be birthed.

In the 1670s a Plymouth resident would hardly feel any more shared identity with a Virginian then they would someone from Newfoundland or Bermuda - they were all Englishmen in distant colonies, sure, but they lived in different parts of the world, with different trades and lives - and often different religions and different worldviews.

The birth of American culture, as in a unified identity around being from what would become the USA - comes much later than Plymouth or Jamestown.