In Harry Potter and the Sorcerer's Stone, Dumbledore appears at Privet Drive:
A man appeared on the corner the cat had been watching, appeared so suddenly and silently you'd have thought he'd just popped out of the ground. The cat's tail twitched and its eyes narrowed.
As far as I know, the only ways to travel almost instantaneously in the wizarding world are apparition, portkeys, and floo powder. I think we can ignore floor powder in this case.
In most instances of apparition in the books, there is a reference to a loud "crack" sound:
With two loud cracks, Fred and George, Ron’s elder twin brothers, had materialised out of thin air in the middle of the room. Pigwidgeon twittered more wildly than ever and zoomed off to join Hedwig on top of the wardrobe.
And with another loud crack, the twins Disapparated
The door slammed shut and at the same moment a loud crack echoed inside the cellar... revealing Dobby the house-elf, who has just Apparated into their midst.
But then, with a very faint pop, a slim, hooded figure appeared out of thin air on the edge of the river... With a second and louder pop, another hooded firugre materialized.
With a crack like a whip, Dobby vanished.
There was a loud crack, and a house-elf appeared.
According to the Harry Potter Wiki:
Apparition can cause an audible noise ranging from a small faint pop to a loud crack that may sound to Muggles like a car backfiring. House-elves may also Apparate but without some of the restrictions that wizards have. For example, they can Apparate inside of Hogwarts and even the Crystal Cave, where powerful enchantments prevent witches and wizards from doing the same. Also, when they Apparate, the sound is mostly a loud crack.
Finally, according to this answer:
Fortunately JKR provided (most probably unintentionally) a nice explanation about how is this avoided - every time someone apparates/disapparates a loud bang is heard. This bang is most probably caused by the air filling in the vacuum when someone disapparates and the air being pushed out when someone apparates.
I can think of 3 explanations for Dumbledore's silent appearance on Privet Drive:
He is sufficiently skilled in apparition so that he does not make any sound. This would invalidate part of the answer to the question linked above.
He was already on Privet Drive and simply deactivated his disguise, which would most likely have been a Disillusionment Charm.
He did not apparate, but used some other form of instantaneous transportation that is not mentioned in the canon.
So, the main question: Why did Dumbledore not make a sound when he appeared on Privet Drive?