Green’s Dictionary of Slang

big time n.²

(US prison) a lengthy sentence, three years plus.

1939		Howsley Argot: Dict. of Und. Sl.
1958		J. Webb Badge (2006) 302: BIG TIME Time served in any state penitentiary.
1961		M. Braly Felony Tank (1962) 18: He didn’t really trust anyone who hadn’t served big time.
1967		P. Thomas Down These Mean Streets (1970) 312: I didn’t know what had happened to Danny and Billy. Maybe the Bronx had them doing some big time.
1971		E.E. Landy Underground Dict. (1972).
1981		E. Bunker Little Boy Blue (1995) 46: You’ll make the big time yet. Just like your brother. You said he’s in San Quentin?

In derivatives

big-timer (n.)

(US prison) one who is serving a long sentence.

1971–2

C. Shafer ‘Catheads [...] and Cho-Cho Sticks’ in Abernethy Bounty of Texas (1990) 198: big timer, n. – someone doing a long sentence.