We know the distance to the Moon from
Radar ranging
Laser ranging
Measurements at lunar eclipse
Parallax measurements from Earth's surface
Measurement at Meridian Crossing
Measurement of Occultation
and ....
Travel to and around it; manned and unmanned, by the USA, Russia, China, Japan, India as the primary mission executants, with contributions to the missions from (at least) Europe and Saudi Arabia. If it wasn't at the distance determined by the previous methods, one or more spacecraft would have missed it.
At some point you have to accept the accumulation of all this evidence, surely?