We needn’t tell our audience where the monster came from originally, and in gaming it’s arguably irrelevant, but the thought exercise can make the result more interesting. The first question should be whether it exists on purpose or by accident.
In worlds with magic, advanced technologies, or unexplained phenomena, the accidental route is especially viable. This is where many comic book characters originate. There are many possibilities that need little in the way of explaining how the monster came about. It encountered something and now it’s a monster. That’s it. No one is going to say our mutated human isn’t possible.
This raises an important point—accidents happen to pre-existing entities, whether animal or a humanoid species. They don’t generally cause a lifeform to spring from nonliving matter. We can do whatever we want, like having a broom become possessed of life as in The Sorcerer’s Apprentice, but none of us regard that as a monster. It’s an animate object.
This also suggests that plants can become monsters even if we don’t usually refer to them that way, but “monster” implies the ability to interact and to change location, not an inanimate object rooted to the ground. After all, a monster that can’t change location typically isn’t particularly terrifying. We could just stay out of reach or wall it up if desired. Maybe it can move but is tied to its lair, literally or figuratively, for some reason we’d want to reveal. Then again, maybe it has telekinetic powers and can influence people over a wide area, messing with their minds so that they have hallucinations, the most important of those being hiding its true whereabouts—or tricking people into coming near enough to become food, like the sirens of Greek mythology.
The accidental route means our monster having some intelligence is more feasible, if it was once human or another sentient species. Years or even decades in the mutated state could have rendered that intelligence muted. Or the incident could’ve immediately rendered it dumber. Or vastly smarter.
Someone caught in an accident has one advantage—our sympathy. They’re a monster now, but maybe once it was a good person with a family, one it wishes to see but is afraid to visit. It might either scare them or something worse, like feel a desire to eat them because that’s what they do as a monster now, having poor impulse control. The monster may recall their past life and be hostile precisely because that old life is gone. This gives it motivation, discussed more below.
Who Caused It?
We’ll need to decide who and/or what caused the accident. Readers want to know such things once one is mentioned. SF offers countless ways for this to happen, from alien weapons, physics gone awry, chemical experiments, or space phenomena. In fantasy, magic, otherworldly creatures, or other supernatural elements are likely sources.
Not all accidents just happen. Some are the result of whatever pursuit someone had, such as trying to manipulate matter or subdue forces. This is a good chance to dream up a scenario that led to the accident. We may have a story to tell as a result. Other characters crop up. Maybe our monster is the one behind the accident but blames someone else. Another option is for someone to have been purposely exposed to something that is intended to kill them but which results in a monster instead. Then there’s the innocent bystander or even a hero who meant to stop an atrocity but is now a monster.