Could it be done? Both franchises need to bend a little. I look at the technological levels and tech level 9 occurs in the 1990s, this is also where the first jump drives are invented. So the timeline looks much the same in our World until the 1980s when the first fusion power plant goes online, air/rafts are developed and US troops are equipped with laser carbines. Grav tech allows easy access to space and Moon base Alpha is set up using the Eagle Transporter, grav plate technology allows the inhabitants of the Moonbase to experience a full 1g while inside the base, but still leap and bound when they go outside in their spacesuits.
On September 13th, 1999 while poking around some Ancient ruins, a massive Jump drive is activated, and Earth's Moon jumps to the nearest star system, naturally since the Moon is too close, they can't control where the Moon jumps to, typically it jumps into various orbits around different exoplanets. If they want to get back to Earth, they have to figure out how the jump drive works, and this sends them to a bunch of different planets.
On September 13th, 1999 while poking around some Ancient ruins, a massive Jump drive is activated, and Earth's Moon jumps to the nearest star system, naturally since the Moon is too close, they can't control where the Moon jumps to, typically it jumps into various orbits around different exoplanets. If they want to get back to Earth, they have to figure out how the jump drive works, and this sends them to a bunch of different planets.