@FarSideOfSaturnI was able to get to the center by joining a random player that was 3200 LY away from the center (so don't consider my request anymore). I warped once to another system and the two trophies popped. Thanks anyway to you for helping others!
A tip for people who want these trophies quicker "by themselves" rather than keeping warping for ages (I know it's not really legit that way and there is no real satisfaction doing so but..): keep joining random players from the main menu and once you arrive in their system, check the galactic map to see how far you are from the galactic center. If you are too far (like 500,000 LY) just leave the session and repeat. You might get lucky like me and find someone really close (around 3200 LY for me). Then just warp once to the closest system and the trophies should pop! For that you need the hyperdrive and at least one warp cell (follow the awakenings mission until you are able to craft a warp cell).