Sorry to have to say... it is definitely a modern-era Civilian usage "Fashion-clothing" imitation of an actual US Navy button. Compare it with the photo of a real US Navy button, below.
Differences between your civilian imitation and the true Military-issue one:
Rounded-top wings instead of pointed-top wings,
one or both valleys between neck and wings is U-shaped instead of V-shaped,
"weakly-stamped" detail instead of crisp sharp detail,
eagle's beak looks tiny like a bird's beak instead of an eagle's large powerful beak,
eagle's belly is fat/bulging,
rope encircling the emblem does not pass through the ring on anchor's top.
Lastly... unlike Military-issue buttons, which must be thick sturdy construction, civilian Fashion buttons usually (but not absolutely always) have a cheap thin iron/steel back, which is often rusted out or completely missing on dug ones... as it is the case with yours.
The other button photo below doesn't show your exact version, but is included to show "waekly-stamped" detail.
