I originally posted this as Kieran, at RPG-D and at my own Harry Potter RPG's forum. But I thought this would be useful for Harry Potter fanfiction writers in general as well.
There are countless ways you can perfeclly easily bring a muggle main character into any Harry Potter story or RPG & have a whole world of possibilities open for it - even if they don't know or never learn about magic's existence! They can know or learn, of course. Just, they really don't need to in order to be endlessly and colourfully written to a muggle's full potential.
If interested in how I connected my muggle characters to the HP universe, see the Wolff family.
IDEAS FOR MUGGLE CHARACTERS IN THE HARRY POTTER UNIVERSE
X A muggle can come across a magical creature somewhere in the world and begin to study it. Even just that can provide a lot of interesting and colourful events without the muggle gaining any knowledge of magic's existence. (You know, not all creatures classified as magical, actually have magical powers. And the muggle myths and books...