If you're looking for a quick way to escape from danger (I know I do, because I always start fights with everyone I really shouldn't), then you need to find and capture Dogen in Palworld for his awesome teleportation skills.
Where to find an oil rig stronghold in Palworld!
Dogen is a neutral Pal that can only be found on Sakurajima Island. There will usually be a few of them walking around the Sakura Dancing Shrine in the Cherry Blossom Forest at -619,224. These Pals are usually lvl 45+, so you'll need to be prepared for a fight.
To catch a Dogen, you need to bring Dark-type Pals. When it comes to this type of Pal, Astegon is the best of the best. You can also add Bellanoir, Blazehowl Noct, and Frostallion Noct to the team.
When it comes to gear, make sure you have good armor. If you don't have Plasteel Armor, at least try to craft Pal Metal Armor to keep you safe. A Hyper Shield would also be a great addition to your protection.