You recognize George Washington as American because of the flow of history not because today’s American are pure racial descendants of George Washington. You (and everyone else) subconsciously associate things like the American constitution, the language they speak, educational, cultural themes and of course territorial association as “American”. From a modernist view applied consistently.. .there would be no such thing as an American. It would a
of fiction of purely ideology. Yet Americans do exist.
Even ethnic groups to various degrees are like American identity. The main difference with ethnic groups is the changes and assimilation happen much slower. We can still identity an ethnic German as German in large part because they speak an evolved version of the German language not because they are pure racial descendants of ancient Germans as the Nazis fantasized. Even Angela Merkel was partially of Polish heritage.