No later than 1974, and possibly earlier.
In 1974 Bill Kaysing self-published his book We Never Went to the Moon. That book has been the blueprint for Apollo conspiracism to this day, and many of Kaysing's original claims, though of course debunked long ago, still pop up in blog posts etc.
Some consider a scene in the 1971 James Bond film Diamonds Are Forever to be an allusion to faked Moon landings. In this scene, Bond runs across a simulated lunar landscape in a secret lab. Conspiracists say this is Ian Fleming's revelation of faked Moon landings, but the scene was written only for the movie and does not appear in the book, which was written in the mid-1950s anyway. It is unclear what role of the simulated lunar surface plays in the film's plot, so it's unclear that it was meant to suggest faked Moon landings; it may have been training simulations such as those carried out extensively at NASA. Screenwriters Tom Mankiewicz and Richard Maibaum passed away before I could interview them, and I have not been able yet to contact director Guy Hamilton.
According to some of the Apollo flight crews, there were hoax theories circulating at the time the missions were being flown, some as early as 1969. I don't have any corroborating documentary evidence for them. Kaysing's book claims Dutch newspapers broke the hoax story shortly after Apollo 11, but no documentation can be found to substantiate this.
