In Trigon: Space Story, you're told to leave the first system pretty early in the game, but that's a huge mistake. You are not yet ready to deal with the gatekeeper or other enemies in other systems. You will be ready after about two months in the game if you focus on leveling up your ship and crew.
Don't try to go to the next system until you have at least five crew members and have all of the ship systems installed. Your crew should also all be at least level 2, and you should have four operational weapons and at least one drone.
Even then, it's pretty hard. Although we were able to move over when we had all of the upgrades and a full crew, it was a challenge. An important upgrade is the fully upgraded sensor, because then you can locate the stations which can ultimately save your life.
We recommend changing ships and returning to the first sector to upgrade it and build wealth.
For more on Trigon: Space Story, why not check out What's the difference between Trigon: Space Story and FTL? or Is there multiplayer or co-op in Trigon: Space Story? Here on Pro Game Guides.