Perhaps, they were certainly foundational in establishing traditions that are now part of American culture, but even 1600 is young compared to many, if not most, European countries

The Franks made Paris their capital in the 5th century, so that still ~1100 years earlier

The Germanic people exists in records from the 1st century

Whether you can consider Spain as originating from Hispania of the Roman Empire, which would place it in the BCs, or you are more conservative and say that it doesn't count until after the reconquista from the Umayyad, we're still around the 10th or 11th century

As for Italy, we're again in BCs with the Roman empire

So yes, in comparison to many European countries, the US is a very young country