behind the eight ball

[Mullins, Bill]

OED has 1932 for "eight ball" and for "behind the eight ball"

"McKechnie To Need Luck As Braves' Pilot" (by NEA Service)
Wisconsin | Sheboygan | The Sheboygan Press | 1929-12-19 Sports Sec. p 1
col 4.
"Bill figures he can finish behind the eight ball with any kind of a
ball team, even the present one, so there is no harm in trying out young
talent as there is nothing to lose beyond last place."

"WORDS NOT WHAT THEY SEEM"
New York Times; Jul 19, 1931; Magazine Sec p. 18 col 4.
"Behind the Eight Ball -- In a tough spot."