Actually, Thanksgiving is a much older European tradition, and did not first originate when the Pilgrims had managed to cross the Atlantic, and survive their first winter.
“Erntedankfest”, (literally, “Harvest-thanks(giving) -celebration (or festiva)l”), as it is known in German, is commemorated in many churches on the first Sunday in October. It was a very widespread European custom, which the pilgrims took with them. Subsequently, in America, it has been greatly embellished upon, and developed it’s own unique (esp. culinary) customs and traditions.
It’s also stil practiced in England: In Britain it’s called Harvest Day, although it’s a lot less of a big deal. While we usually take a few non-perishables down to our local church and enter our autumn vegetables in competitions, Thanksgiving in North America is a much more plentiful and extravagant affair.