APA says that "U.S." should be typed out with periods if the abbreviation is being used as an adjective. If you are using this "common" abbreviation, do you need an earlier parenthetical explanation of the abbreviation?
In other words, if the progression of the text is:
"He lives in the United States ... He is a member of the U.S. Navy."
should it be: "He lives in the United States (U.S.) ... He is a member of the U.S. Navy."