You may want to take a look at this 1901 entry for Pembrokeshire but no guarantees it’s the right one
Thomas Cousins 37 farmer
Ada 37
William 16
Bertie 6
Piece 5125 Folio 57 Page 13
A possible as unable to find another living Thomas (father/farmer) in Wales with son William rightish age. William not with birth family in 1911.
This William left for the States in 1914
Source
New York Passenger Arriva...(Ellis Island), 1892-1924 Roll 2346, vol 5375-5377, 10 Jul 1914
William Cousins age 30 arrived on 10 Jul 1914 Ellis Island, New York City, United States going Shamokin, PA., U.S.A. States single from Great Britain, Welsh, father Thomas Cousins a farmer, Pembroke.
One William to follow or rule out. Link below to military draft registration 1917/18 has his signature, compare with signature on marriage cert to Annie, see if possibly same William? Also includes census.
Familysearch
https://www.rootschat.com/links/01rzj/ https://www.findagrave.com/memorial/52097148/william-cousins marriage & 3 children born in USA.
Added: Annie & children are in Llangeinor, Bridgend on 1921 free index. Also in household is Jacob Rees Thomas & wife Rachel Alice nee Smith (sister of Annie) The full record would have all info.
Cas