Was the god Pan once seen as an all father?

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.

Wasn’t Pan the goat with a human’s head who played a flute?

My understanding was that Pan was one of the Greek gods. As such, he was not an all-father figure. He was in charge of something, as were they all. In the case of Pan it was nature and pasturelands. I’ve also heard he was associated with fertility and the season Spring. But none of these is really an all-father aspect. He isn’t said to have created all these things, but was in charge of them. However as @SavoirFaire there may have been various cults that looked on Pan as the God…the creator, the all-father.

@Dutchess_lll Pan’s instrument was technically a Panpipe—it had multiple pipes in a row kind of like a harmonica but was a woodwind instrument rather than a reed instrument.

I would agree that he was an earth god but not a mere faun. The Goat of the Woods is not to be reckoned with—not the supreme God but just as powerful by our standards.

Monotheism, the idea that there is one and only one god, is said to originate with Zoroasterism about 4000 years ago.
Every mention of Pan I find suggests he is one of a host of gods, not an ‘all father’.