The National Matches were started at Sea Girt in 1903, held at Fort Riley, Kansas, in 1904, and moved back to Sea Girt in 1905 & 1906.
The National Matches were first hosted at Camp Perry, Ohio, in 1907.
My guess is that, if the photograph was taken at the "National Matches" in New Jersey, it would date from 1905 or 1906. However, from what I understand, the Sea Girt Ranges continued in use for Rifle Matches by the N.J. National Guard and other states, at least, into the late 1930s.
Early (circa 1903) photos, taken at Sea Girt, show competitors shooting Krags.