(Yes, of course I know that’s not the Enterprise-D and that TNG came out in 1986, but you try making a better debunking joke.)
My favorite debunking is an old YouTube video called “moon hoax not” where a filmmaker explains that the due to technology limits of the time, faking the multi-hour live broadcasts in slow-motion, which millions of people were watching, would be impossible without there being telltale signs of it being spliced film (the splicing, film grain, etc.). Since slow-mo video (distinct from film; TV broadcasts were video) at the time could not play back more than a few seconds of footage, at most, it would have to be high-speed film played back at normal speed. Assuming you could find or make a high-speed camera fit to task. While the first landing had awful video quality, later missions had much higher quality and the film fakery would be impossible to completely hide. People these days massively overestimate the video (and film) technology that was available in 1969. (IIRC. It’s been years since I’ve last rewatched it.)
Edit: TL;DR: Perfectly faking the multi-hour uninterrupted video broadcasts (i.e., either inventing slow-motion video that can last hours, or perfectly passing off a multi-hour film as video) in slow-motion would have been significantly more difficult than sending humans to the moon with 1969 technology.
The reason the conspiracy exists is because the video footage is staged to match the audio. Obviously there wasn’t a camera crew on the moon.