After this guide was written, a mod by @Shrub was released — use it:
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=3583412086
If for some reason the mod doesn’t work, you can use the old method below.

1. Install and enable the mod Warp Menu (you can remove it later).
   
   
2. As soon as the character gains control, press ESC and use the Warp Menu to teleport to one of the Echo rooms:
   
   • Shaded Citadel - A08,
     
   • Farm Arrays - B01W,
     
   • Chimney Canopy - C12.
   
   
3. Listen to the dialogue (cannot be skipped).
   
   
4. After the cycle ends, repeat step 2 for each Echo room. The last room determines which region you’ll end up in:
   
   • Shaded Citadel → Torrential Railways,
     
   • Farm Arrays → Coral Caves,
     
   • Chimney Canopy → Sunbaked Alley.

There are many non-working methods; here’s a working one:

1. Install and enable the mods BeastMaster and BeastMasterPupExtras (you can remove them later).
   
   
2. Do "Fast Echo collecting".
   
   
3. Create a pup:
   B key → Slug icon → Slug icon → ALIVE slug icon → PINK slug icon → Shift + LMB on the screen next to you.
   If slugpup spawns as an adult, you didn’t hold Shift.
   
   
4. You can spawn multiple pups to pick a good looking one.
   
   
5. Feed the pup, then sleep with it in the shelter.

Important! Always take the pup off your back when talking to an Echo (you can hold it by hand or drop it on the floor), otherwise the slugpup might not teleport, and the game will still save. If this happens, restore the game from an automatic backup or create a new pup.

Unfortunately, after any ending, the slugpup will still disappear. Other than that, playing with it works without bugs.

Give it a like and add it to your favorites so more people can see it. Thanks!