I scarcely remember this animated series.
The gist of it is in the title: Earth vanishes (I can't remember the reason now but it was probably explained) and the only surviving humans were two astronauts on an interstellar spaceship. They decide to explore space and meet up with different aliens, hoping that one day they'll find out what happened to Earth.
It might be the anime adaptation of the French comic Valerian et Laureline. The anime doesn't follow the storyline established in the comics.
In the anime, when Valerian comes back from his first spacetime mission with Laureline, they find out that Earth has vanished, and soon realize that they are the only two Humans left, and no one even remembers anything about Earth or anything associated with it.
In the end, they find out that it was a conspiracy by most of the leaders of Earth, who also happen to lead the spacetime agency, to alter the past and set themselves as absolute rulers of the planet.
You can find the whole anime on Youtube on the Valerian and Laureline official channel.
