How can I instantiate a prefab from a static function?

The prefab as to be static as well in order for you to use it in your static function.

Yes, that's the static price you have to pay. Assign it manually via code somewhere. Statics are generally evil.

I would prefer to have it as a static function rather than create a reference on almost every script

This sounds to me like you're lazy. Are you sure you must use statics? - See this, jump to good coding habits section and read when should and shouldn't you use something static.

If it's a must, and you're dealing with say, a GameManager, or AtlasManager, etc. Then at least use a Singleton.

You mean instantiate a prefab, and have a variable reference it? How about doing it in Awake?

See this (Resource.Load), and this.

"I've never really used static functions before, but I felt that maybe my objects had too many references and that it was starting to look untidy." indeed if you use the grid "system" below to be grandiose, you will only have that one static (unless you have some others that do say math or who knows what), and then you will be able to have no statics whatsoever, other than that. so it's a good intro when you're just learning.

mis-use of statics by beginners drives me frickin nuts. you will often see me lying on here "Oh, statics have been removed from the new Intel chips, you must not use them now." to help beginners :)

as Vexe intelligently alerts us, static prefabs are the like are a nightmare and not to be involved with.