According to Quora it takes 5 minutes, with a willing participant.
Anaesthesia that's injected right before an operation can knock you out in about 30 seconds (and until then you could still struggle, technically speaking), but that's a thick-ass tube of drugs they're pumping inside of you. Some vapours from a rag is going to do jack shit.
Cue Scotty, Mr "miracle worker", quadrupling his estimates:
https://www.youtube.com/watch?v=t9SVhg6ZENw