Past, future, far future.
Abby began their life as a small sample of a mysterious black substance that "leaked" out of a rift torn open in spacetime, as the result of a failed "interdimensional gateway" experiment. Not much is known about their true place of origin, and they have little to no memory prior to this event. They spent the first 10 years of their life in captivity raised by researchers, gradually learning to mimic humans and developing an unruly personality. However, the treatment they received was cruel and unethical, leading them to escape in a violent jailbreak. During their "teen" years they experimented wildly with their form, living in the woods and inspiring local legends with their frightening appearance and general avoidance of humans. Eventually they settled on a form that felt "right."
In present day, Abby spends most of their time meandering through dark spaces and dimly lit city alleys, stealing food from wherever they can, being generally unsettling and scaring people, and occasionally killing anyone that has the misfortune of catching them in a particularly bad mood. They are primarily nocturnal and sleep during the day, at least until they meet Vivian. More on her later.
Being effectively immortal, Abby does not really age, but rather continue to increase in size over time. They become kinder, but also increasingly less attached to maintaining a human form, until eventually becoming a roiling dark mass of tendrils and eyes.
In the far future, to avoid subsuming the Earth, they launch themself into orbit and become the planet's second satellite, known as the Abyssal Moon. Humanity has largely become less paranoid in this time, and establishes a sort of mutual understanding with Abby Moon under the terms of "don't bother us, we won't bother you." Having brought various communication / broadcast devices with them, as well as a personal computer, they begin to garner an internet presence and stream video games frequently in an effort to stave off the isolation and boredom of eternity.
The majority of their story takes place during the present day, that is, during their 20s, but their origin has lasting effects on their sense of self and their relationship with others.