If he is the Anthony W Brown age 32 (1898) with wife Olive in 1930 NY Allegany Co census, son Robert is 2 yrs old b. NY all the rest of family born PA, including older children and reported yes WW on Veterans question. There is an Anthony Brown with birth date April 20 1894, d. 1980 in Manatee Co FL. If these are the same man and your Anthony, then order copy of death certificate, may have question abt military service. He should have had a SSN so order a copy of SSN application for parents names and placed born with birth date reported. Looks like he would have been PA when enlisted so look at their archives as well as county records where he lived after war. For him to be too young and needed to lie about age to enlist he would have had to have been born after abt Sept 12, 1900. Look for him in 1920, 1910 census for age comparison.
20% of records survived the 1973 fire at NARA, so still try to get service records from there. www.archives.gov