Green’s Dictionary of Slang

(US) superlative, outstanding.

1905		‘West Point Sl.’ in Howitzer (US Milit. Academy) 292–5: Cold Max — Perfect; all that can be desired.
1952		W. Sheldon Troubling of a Star 248: If the Wing was making a max effort, he wanted to be in on it.
1968		Current Sl. II:3 4: Max, adj. Best, good, great.
1989		Hackworth & Sherman About Face (1991) 99: We requested max harassment and interdiction.
1999		Dr Dre ‘Some L.A. Shit’ 🎵 Bust caps for my max crew, at Fairfax / who used to wear Air Max shoes, that’s true.