Why people take NAC before drinking
The 2021 paper's rationale is glutathione. The authors write that when a lot of ethanol is consumed, glutathione stores drop, and that NAC, as a glutathione donor, might lessen oxidative stress during alcohol metabolism. They cite animal work in which rats were pretreated with NAC. That is why the "before drinking" idea is common. It is the reason researchers gave, not a result.
The human trial itself did not give NAC before the first drink. It was a randomized, double-blind, placebo-controlled crossover study. Forty-nine volunteers finished it. They drank the same beer until a breath alcohol of 0.1 g/210 L, then received identical-looking capsules of NAC or lactose placebo. The other treatment came at the second visit. The next morning they filled out a Hangover Symptom Scale. The NAC amount was 600 mg capsules, one to three of them depending on how many beers they had drunk, so the dose the investigators used was 600 to 1800 mg. This page does not recommend that dose or any other.
On the main result, the paper says no significant difference was found in overall hangover scores. The authors' conclusion is: "Although no difference was found in the general hangover scale scores, the study was suggestive of a gender difference with females having improved hangover symptoms after NAC use." They also say participants reported no serious adverse effects. Complaints they recorded after the NAC capsules included gastrointestinal symptoms, headache, rash, muscle twitches, and insomnia. Headache and gastrointestinal symptoms were also reported after placebo.
Sources: Coppersmith et al., 2021: NAC and hangover symptoms, a randomized trial