There are a large number of factors involved. It was Durin's Day and the last rays of sunlight fell on the rock, revealing the key. And they had the key, Gandalf had gotten it from Thorin's father.
Chat with our AI personalities
The last rays of the sun on Durin's Day fell upon the wall and revealed the keyhole.
On Durin's Day the last rays of the sun struck the appropriate spot on the wall when the Thrush knocked. This was foretold on the map in moon letters.
Bilbo thought the dragon would be there any second so he told Thorin to shut the door. Which he did in the nick of time.
They called it the Front Door. The Back Door was the cave where the party had sheltered from the storm.
Durin's Day indicates that the dwarves can open the door with the key on the last moon of Autumn.
When the Dwarves first come to visit Bilbo there is a bit of slapstick humor. At one point there is a loud knock on his door which causes him to get angry and open the door with a jerk. Four Dwarves come crashing in, one on top of the other. Gandalf gets a good laugh!
A hobbit barrow is referred to as a 'smail.'
They all look different They have different colored hoods.