Thomas was born in 1904. He is the son of Thomas Archer.
Sources
"United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:ML7N-LL6 : accessed 30 December 2018), Thomas Archer Jr. in household of Thomas B Archer, Township 5, Craig, Oklahoma, United States; citing enumeration district (ED) ED 31, sheet 8B, family 7, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 1249; FHL microfilm 1,375,262.
"United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MJ9H-D4G : accessed 11 August 2020), Thomas Archer in household of Thomas B Archer, Venita Ward 1, Craig, Oklahoma, United States; citing ED 16, sheet 5A, line 37, family 107, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, 1992), roll 1458; FHL microfilm 1,821,458.