The script should be fine. If you want to do it in a cutscene as an intro, you can use a parallel event as well. It just takes a bit of clever eventing without the need of additional scripts to gradually increase volume. Point being to just make sure that the player makes a specific association with however you choose to do the sounds with what ever chases them. So that also means dont change music across every map, but different styles of music for inside or outside, or a canyon, desert, etc, those kinds of changes should be fine.
Slightly off topic, monsters as important as this are Main Characters, and most main characters, even in films, get their own theme song. This style can just be used to function like a theme song, just intended to make players go poopie in their pants.