Green’s Dictionary of Slang

(US/UK teen) an all-purpose term of approval.

1964		R. Abrahams Deep Down In The Jungle 231: Junkie looked down on him and said, ‘Safe’.
1996		CyberBraai Lex. at www.matriots.com 🌐 SAFE, MY MATE: It is hard to trace the origin of this widely-used phrase, but the ‘mate’ indicates an Australian connection. It means ‘okay’ or ‘fine’ at the end of an exchange.
1997		N. Barlay Curvy Lovebox 45: Safe man.
2000		N. Barlay Crumple Zone 41: J’na mean. Safe. Bruvvers an’ Geezers innit. Bitches an’ Whores. Innit. Wicked. Yeah.
2006		G. Malkani Londonstani (2007) 3: Yeh, blud, safe, innit.