Are you born an avatar?

Question

This may be an obvious question but if you do math according to this question you get the average age of avatars to be 54ish years. This seems quite short. Therefore could theoretically be more then one avatar living at a time and Raava simple moves on at ones death.

Does Raava pass onto the next avatar at death and birth or at some other time?

Answer 1

Wiki explanation of the Avatar Cycle

Although it has never been explicitly stated that the next avatar is born immediately after the previous one dies, it is heavily implied that the Raava merges with the next Avatar at birth, or at least very near to birth:

• Air Avatar Yangchen is the oldest named reincarnation of the Avatar, followed by Water Avatar Kuruk, Earth Avatar Kyoshi, Fire Avatar Roku, Air Avatar Aang, and finally Water Avatar Korra.
• Yangchen died circa 345 BG (Before the Air Nomad Genocide, at the start of the 100 Year War). It is unknown how long she lived.
• Kuruk was born c. 345 BG and died in 312 BG, living approximately 33 years.
• Kyoshi was born in 312 BG and died in 82 BG, living 230 years and is confirmed to be the longest living Avatar.
• Roku was born in 82 BG and died in 12 BG, living 70 years.
• Aang was born in 12 BG and died in 153 AG, existing for 166 years.
• Korra was born in 153 AG.

It is a fair assumption that each Avatar is born, lives, and dies as a host of Raava. There is no evidence that Raava is ever disconnected from any Avatar, except for when Raava is forcefully removed and killed at the hand of Vaatu in 171 AG.

 

If you want to delve in to conjecture as to the ages and number of Avatars:

Wan was born in 9850 BG. Aang died in 153 AG. Aang is the 182nd Avatar. 182 Avatars lived in 10,004 years, making the average life of each avatar 54.967, in practicality 55.

Sometime before Aang, tradition developed to make the Avatar known at age 16, at which point the Avatar entered into training for the other three elements until they become a fully realised Avatar. We know that before the Avatar turns 16, the identity of the Avatar is not revealed to the world, or even the Avatar himself. It is quite likely this is primarily done out of concern for the safety of the Avatar. Certainly, Fire Lord Sozin is not the first person to attempt to kill the Avatar before he comes into his power. It is therefore reasonable to assume that some Avatars died quite young, which would drive the average age down quite a bit. Avatar Kuruk is evidence enough that not all Avatars live to old age. There is no reason to assume that simply because the few Avatars we know of lived for the most part to old age, that the rest of the Avatars would live that long too. In fact, we know our sample includes the longest living Avatar and an Avatar that spent 100 years frozen in a iceberg. That's an incredibly skewed sample even without knowing anything else.

Answer 2

Reincarnation of the Avatar is definitely a thing

In Book 3's "The Avatar and the Fire Lord", Avatar Roku shared with Aang a memory of his past, which involved his death. Immediately following that, Aang saw himself as a newborn baby. From the Avatar Wiki transcript:

With the rock avalanche just moments away from swallowing Roku, Fang flies down, and wraps himself around Roku. The wave of ash and rubble cover the two completely, killing both of them. Fade to a bright light, as the camera pans to show an arched window frame. A baby's cries can be heard. The camera pans down to show a smiling born infant.

Aang: Who's ... wait, that's me, isn't it? [Cut to a long shot of three Air Nomads. A nun holds up the baby to the light while two people, presumably the infant's parents, stand in the shadows.]

See also: Are other human spirits reincarnated in the world of Avatar: The Last Airbender?

Raava is permanently bonded to the Avatar and stays with them throughout each lifetime

In The Legend of Korra "Beginnings, Part 2", Raava permanently bonds with Avatar Wan. From the Avatar Wiki transcript

While still static, Wan lights up briefly, showing Raava's form inside his chest. He puts his right hand behind him, causing the energy of the southern spirit portal during Harmonic Convergence to flow though him, basking him in blue light, as he permanently merges his spirit with Raava's. […]

Raava: We are bonded forever.

An old Avatar Wan laments at the fact that he couldn't defeat evil in his lifetime. Raava responds:

Don't worry. We will be together for all of your lifetimes. And we will never give up.

We see that the Avatar can be identified from an early age

The monks knew Aang was the Avatar since he was a child:

You chose them from among thousands of toys, Aang. The toys you picked were the four Avatar relics. These items belonged to Avatars past. Your own past lives.

_{—Monk Tashi, Book One Episode 12 The Storm}

Korra too was identified as the Avatar when she was a few years old, but unlike most Avatars, it was blatantly obvious since she could bend multiple elements from that age.

So I think it's safe to say that Avatars are who they are from their birth.