So I'm writing a science fantasy WiP and I'm unsure how to introduce the characters and their background, day-to-day life if that's all going to change after the inciting incident.
So in question format, is it good/bad/neutral to introduce a character's day to life if that's going to change, and if it's bad, what is the best way to introduce how a character fits into a world?
In the Hero's Journey, this is called The Ordinary World, and it's important to establish.
The Ordinary World is what the Hero must leave to go on the Journey. This World may be good or bad, whole or broken, the desired status quo or something which needs to be fixed, but it's where the Hero starts. The point of the Journey may be to get back to this World with the Elixir of Knowledge. It may be to restore a former World. It may be that the Journey itself changes the Hero so much that s/he cannot return to this World, and it comes to symbolize innocence or childhood. All these are fine.
Having at least one day of "ordinary day-to-day stuff" is common and very workable. It helps the reader appreciate that the Hero is leaving all this behind to go on the Journey. If the Hero loves this World, then making the choice to leave it is literally the first step of the Journey.
My favorite performance of this task was Magic Kingdom For Sale--Sold! by Terry Brooks. It spends about a chapter in the Ordinary World and then goes back a couple of times.
To answer your question: It adds depth to the characters. It is good.
Can it be overdone? Yes.
If your hero's life is going to be "drastically changed," you definitely need to introduce the "day-to-day" life before that change. But do so "briefly."
That is as a reference point from which the hero's life is changed. Otherwise, there's little point to your story.
