According to the 1871 census, Mary J was the first born:
1871
RG10/2819 160 28
Castle Church, Staffordshire
26 Castle St
Joseph Bowers, head, 27, Railway Labourer, b. Lancashire Eccles
Elizabeth, wife, 26, b. Cheshire Hudkinton
Mary J, dau, 4, b. Staffordshire Stoke
Joseph, son, 3, b. Staffordshire Castle Ch
Elizabeth, dau, 6 mo, b. do.
I'm pretty confident I've found the correct marriage but to ascertain Elizabeth's maiden name you'll have to order the birth certificate of one of the children.