Looking for them just outside of the forest seems a good plan... Mine was on a beach attacking herbivores... Lots of narcoberrys are a must and tonnes of meat, preferably prime. My friend went to tame one, i used by quetz to pick up a big stock of berrys and prime meat.
Some tames i take fence foundation, walls and doorway/doors to prevent dinos from interfering
1. Make a bear trap and crossbow with tranq arrows or a longneck with tranq darts
2. Go into the Redwoods on any map, DO NOT fly on anything because the Thylacoleo can jump out of trees and take out your flyer, on Scorched Earth it spawns pretty close to the Wyvern Trench, so be careful
3. Look for a decent Thyla, I’d recommend 145-150 you can usually find them chasing a Gallimimus
4. Place down a bear trap and lure the Thyla into the trap
5. Repeatedly shoot it in the head with whatever you’re using to knock it out
6. Once it’s knocked out, place COOKED meat in its inventory, it’s the only creature that prefers cooked meat over raw. You can also use Extraordinary kibble, which is produced by Magmasaur, Yutyrannus, Deinonychus, Rock Drake, Wyverns and Hespornis(golden egg)
7. Name your new Thylacoleo! It provides a bleeding effect to any wild creature, it can also climb vertical surfaces and pounce on creatures, it’s one of the best cave clearers out there!