You can describe your ancestor who traveled to America on the Mayflower as your forefather.
Use the noun forefather to talk about a relative in the distant past, usually a man who goes back on your family tree several generations. Your great-great-great grandfather is your forefather, for example. You can also describe the founder of a tradition or style as a forefather — some people think of Chuck Berry as the forefather of rock n' roll, for example. Fore, "before," combines with father in the word forefather.