The real conspiracy is hiding the fact that the US government has had FTL and time travel technology since the 1950s. The first sightings were USAF space-time machines being tested on backwards jaunts of about 5 to 10 years. Navigation was a problem in the early days.
Why keep it a secret? Would you want the Soviets to get that technology or face average Americans rushing off into the void to claim their own planets? Real smooth way to crash the economy and get a bunch of people lost in space and time.
But now that NASA has gone public with their starship program and the astronomers have started naming ‘earth like’ extrasolar planets it’s only a matter of time before they announce a FTL breakthrough. How do I know all this? I pulled it out of my ass and why would my ass lie to me?