Green’s Dictionary of Slang

(US/Can.) absolutely bereft of; usu. used of some form of commodity.

1942		N. Algren Never Come Morning (1988) 85: ‘Why didn’t you take a bottle off your own shelf? You deal in milk.’ [...] ‘We was fresh out, Captain.’.
1957		Kerouac On The Road (1972) 132: Dean [...] stole three packs of cigarettes without trying. We were fresh out.
1960		J.D. Macdonald Slam the Big Door (1961) 122: I’m fresh out of alternatives.
1968		S. Gore Holy Smoke 9: Not to mention they were just about fresh out of tucker.
2001		S. King Dreamcatcher 100: I’m fresh out of ideas.