slang shortening of debutante, by 1920 (Fitzgerald). The derived sub-deb is attested by 1917.
Entries linking to deb
debutante n.
1801, "female stage actress making her first public performance," from fem. of French debutant, noun use of present participle of débuter "to make the first strike" (in billiards, etc.), from debut (see debut). In reference to a young woman making her first appearance in society, from 1817.
sub-deb n.
"girl who will soon 'come out;'" hence, "girl in her mid-teens," 1917, from sub- + deb.