It’s fine if your ancestors did not arrive on the Mayflower. You can still celebrate Thanksgiving. Remember that we don’t get to choose our ancestors, but we do get to choose how we research them. With that in mind, locate as many records as you can; analyze the records as best as you can; and learn as much as you can about the time of your forebears, the records that were kept, and the terminology that was used.
Do that and your research will benefit–whether your have ancestors on the Mayflower or not.