Sorry to have to say, that one is definitely a crude civiian-usage imitation of an actual US Navy button. Collectors of Historical Military buttons call those a "Fashion" button, manufactured for use on fancy civilian clothing. The major ID-clues for these imitation Navy buttons are:
Round-topped wings,
rope (encircling the emblem) does not pass through the loop on the anchor's top,
the small details of the emblem are "weaker" than on actual US Navy buttons, which have sharp/crisp detail.
These "Fashion" buttons are found on imitation Navy "pea-coats" for sale today. They can also be purchased at sewing-supplies stores like JoAnn Fabrics & Crafts.
Compare your "Fashion" imitation navy button with the actual US Navy button in this photo, noting the actual's very sharp-topped wings, and the rope going through the anchor's loop, and the crisp detail of the stamping (like the fine lines inside each feather).