Out of Universe
In his The Folklore of Discworld, Terry Pratchett confirms that knowledge that the astronomical composition of the Discworld (e.g. disc/elephants/turtle) is known by everyone on the disc, albeit with some small exceptions.
The absolutely central, incontrovertible fact about the Discworld is that it is a disc. At least, it’s incontrovertible unless you adhere to the Omnian religion, in which case you must controvert it like billy-o
Clearly, fragments of information have drifted through the multiverse and taken root here and there. But the full and glorious Truth is known only on the Discworld. The Turtle Moves!
We also have multiple pieces of in-universe evidence from the Discworld novels that show that this knowledge is very widely held.
It has been proven by direct observation.
The Great Turtle was a mere hypothesis until the day the small and
secretive kingdom of Krull, whose rim-most mountains project out over
the Rimfall, built a gantry and pulley arrangement at the tip of the
most precipitous crag and lowered several observers over the Edge in a
quartz-windowed brass vessel to peer through the mist veils.
The early astrozoologists, hauled back from their long dangle by
enormous teams of slaves, were able to bring back much information
about the shape and nature of A’Tuin and the elephants but this did
not resolve fundamental questions about the nature and purpose of the
The Colour of Magic
Ephebian scholars have known it for centuries and have written works that are widely available.
Vorbis shrugged. “The writer claims that the world…travels through the void on the back of four huge elephants,” he said.
“Most curiosity is,” said Vorbis. “It leads the mind into speculative ways. Yet the man who wrote this walks around free, in Ephebe, now.”
Drunah glanced at the scroll.
“He says here he went on a ship that sailed to an island on the edge and he looked over and—”
This knowledge is widespread throughout the 'civilised' world.
That wasn’t poetic imagery but plain fact, since the world was quite
definitely flat and was, furthermore, known to be carried through
space on the backs of four elephants that in turn stood on the shell
of Great A’Tuin, the Great Sky Turtle.
The Wizards know (obviously). They can also directly observe the Discworld through magical means.
The shape around Simon’s head was the world.
That was quite clear, although the glitter and rush of the little lights blurred some of the detail. But there was Great A’Tuin the sky turtle, with the four Elephants on its back, and on them the Disc itself. There was the sparkle of the great waterfall around the edge of the world, and there at the very hub a tiny needle of rock that was the great mountain Cori Celesti, where the gods lived.
Basic schooling on the Sto Plains evidently includes instruction on the nature of the world.
“About the universe is what I meant,” said Albert hurriedly. “I mean, have you ever thought about it?”
“I know the Disc is carried through space on the backs of four elephants that stand on the shell of Great A’Tuin,” said Mort.
The Dwarves are well aware (and have been for some very considerable time).
They say that the fifth elephant came screaming and trumpeting through
the atmosphere of the young world all those years ago and landed hard
enough to split continents and raise mountains.
As for the dwarfs, whose legend it is, and who mine a lot deeper than
other people, they say that there is a grain of truth in it.
The Fifth Elephant
Vetinari, Slant and the majority of Ankh-Morpork's gentry all know.
"Really? Well, we can do without magic for a couple of years, can't we?" said Mr Slant, managing to suggest that this would be a jolly good thing, too.
"With respect," said Ponder, without respect, "we cannot. The seas will run dry. The sun will burn out and crash. The elephants and the turtle may cease to exist altogether."
"That'll happen in just two years?"
"Oh, no. That'll happen within a few minutes, sir. You see, magic isn't just coloured lights and balls. Magic holds the world together."
In the sudden silence, Lord Vetinari's voice sounded crisp and clear.
The Last Hero
Further evidence of the flatness of the world can be seen when people refer to the four cardinal directions.
"It's Rimwards" - The Last Continent
“The dragons headed hubward,” - The Colour of Magic
"You know that tower widdershins of Lancre" - Going Postal
“Oh, a sub-sect of the Turnwise Klatch
philosophical system of Sumtin" - Wyrd Sisters
As to the very specific question of why Granny Weatherwax doesn't know what an elephant is, the reality is that she lives in a very small village and hasn't traveled extensively (yet).
Her knowledge of the world comes from elementary schooling, supplemented by occasional visits from peripatetic teachers, missionaries and the reading of a single journal, the excellent 'Goatberger's Almanack And Booke Of Dayes' which presumably contains the occasional crude woodcut but is highly unlikely to offer much by way of detailed description of elephants.
It's hardly surprising that she's unaware of precisely what an elephant actually is, other than that it's a large weird-looking animal.