How would faking footage be more difficult than successfully launching and building from scratch a rocket into space and landing a human on the moon when it’s never been done before? From a pure probabilistic standpoint, faking the footage would be easier. However, it would be excessive, and I don’t think the US would do all that to keep up with a lie they’d continuously need to preserve for their name. JFK also was one of the good ones.
They did build from scratch a rocket that was capable of landing a human on the moon. We have extensive documentation on the Saturn V and the rest of the spacecraft, as well as artifacts from them sitting in museum, including command modules. Not to mention the retroreflector placed on the moon during the Apollo 11 mission, which is still usable to this day. Faking the footage and planting evidence that convincing would have involved making tech capable of, and actually going to, the moon.