Green’s Dictionary of Slang

1. a robbery, usu. shoplifting.

1933		Ersine Und. and Prison Sl.
1937		B. Dai Opium Addiction in Chicago 196: Boost, the. Shoplifters. Also called boosters or the clout.
1949		Monteleone Criminal Sl. (rev. edn) 31: boost A shoplifting job.
1950		Goldin et al. DAUL 32/1: Boost, n. 1. A successful shoplifting operation. 2. A successful pocket-picking operation. 3. Any successful theft of articles near to hand; (loosely) an automobile theft.
2000		G. Pelecanos Shame the Devil 11: He’d done his share of small-time boosts — car thefts, smash-and-grabs, like that — with his older brother.

2. a stolen vehicle.

2000

C. Cook Robbers (2001) 78: Maybe they were driving a boost, probably were.