Upgrade, Upgrade, Upgrade
There are a lot of different blueprints you can obtain in No Man’s Sky, but the ones you should be focusing on are any that have to do with the Hyperdrive. When you first get this upgrade to your Starship, you can only jump about 100 light years. The first Hyperdrive upgrade lets it jump to 300, and then 1000, and can increase further if you find the stronger, but rarer, upgrades.
The folks who gave you the Atlas Pass that were in that Anomaly, the Korvax and Gek, provide these upgrades. But, you can also get them earlier if you’re lucky. The random aliens you encounter on planets and in Space Stations have a slight chance to provide the blueprints necessary to upgrade. You will have to do quite a bit of resource collection – one of the upgrades requires 1000 Gold and 1000 Emeril – but it’s definitely worth it.
Before you know it, you’ll be skipping over Star Systems 10 at a time.