First things first: being an all-father and being an earth god aren’t the same thing. Zeus, for example, was classified as both an all-father and a sky god. But there were some mystery cults that associated the god Pan with the concept of an all-father. There were as many reasons for this association as there were mystery cults, but at least some of them counted the superficial similarities between the name of the god (Πάν) and the Greek word for “all” (πɑ̂ν) among their reasons.
One might wonder why I call the similarities between the two words superficial. After all, they are composed of the same three letters! But accentuation matters in Greek, not least because it was primarily a spoken language. Πάν and πɑ̂ν are two different words, no matter how much they look alike, the same way that bear (the animal) and bear (the verb meaning “to carry” or “to support”) are two different words no matter how much they look alike.