You have to gradually explore the threats posed by the monster. It can start with something innocuous but unnerving (say a few strange bumps or the sound of chains rattling in the night) and then get harder and harder to ignore.
Assuming the monster has to eat, you could incorporate the bad roommate trope of food going missing. Maybe the protagonist had a big fancy steak they were excited to eat and when they look in the fridge, it's gone. Then later on, you can establish the lib has been actively feeding the monster.
I guess the culmination would be that a person goes missing. Like the protagonist's partner spent the night there, and allegedly had to leave early in the morning, but when the protagonist wakes up, one of their partner's shoes is still in the house.