Highlights

The Air Nomads' annihilation by the Fire Nation may not be entirely true, as there are indications that they could have survived by fleeing or seeking refuge among other nations.
The Fire Nation's propaganda about defeating the Air Nomads could be just that - propaganda. Their supposed victory over the pacifist nation with no army may have been exaggerated.
The Harmonic Convergence event in The Legend of Korra may have reconnected descendants of the Air Nomads with their airbending heritage, suggesting that the lost airbender tribe was always connected to their roots, but needed a catalyst to awaken their abilities.

It's possible the title Avatar: The Last Airbender could have been a misnomer. The series begins with Avatar Aang emerging from a sphere of ice and being told he's the last airbender. Throughout the series, Team Avatar journeyed to various places including all of the air temples to confirm the statement. It would seem that the airbenders, as history tells it, were victims of genocide perpetrated by the Fire Nation in search of the next Avatar.

However, there are many truths that were revealed to be fiction in Avatar: The Last Airbender. Sifting through the facts and plausible probability of the Air Nomads being massacred by the Fire Nation's army, one could conclude otherwise. Though it has yet to be officially revealed whether the Air Nomads survived the Fire Nations attacks, there are a few ways that suggest how they could have.

Avatar The Last Airbender: Benders vs. Non-Benders

Avatar: The Last Airbender finally gives Aang the chance to address the bender vs. non-bender problem in a graphic novel Imbalance Omnibus.

Was Aang Really The Last Airbender?

The dragons who taught the early humans how to firebend were said to have also been exterminated. General Iroh was believed to be the one who killed the last remaining dragons. That turned out to be false. It became Fire Nation propaganda that made General Iroh even more legendary and respected, thus fanning the flames that empowered the Fire Nation to continue its war efforts with more confidence. Uncle Iroh's lie saved the dragons from extinction and rallied the troops, a win-win situation in the Hundred Years War. Uncle Iroh once said:

History is not always kind to its subjects.

The most verifiable evidence regarding the deaths of the Air Nomads from the Fire Nation's attack on the air temples is seen in the Southern Air Temple, home of Avatar Aang and the resting place where Monk Gyatso's skeleton lays. Many of the Fire Nation's troops, empowered by Fire Lord Sozin's Comet, were seemingly defeated by the Air Nomad, Monk Gyatso. This was surely an embarrassing defeat as Aang affirms the Air Nomads were pacifists and had no army. Yet, the Fire Nation tells the story differently. They state that their army defeated the army of airbenders. This sounds like typical war propaganda just as Iroh "annihilated" the dragons. Even if the Air Nomads were at a disadvantage in terms of power and war skills, they had something the Fire Nation didn't, which is also how they could have survived.

How the Air Nomads Could Have Escaped Annihilation

Unlike the firebenders, the airbenders could fly by various means. With their temples erected high up on mountains, the Fire Nation had only one way in and out of the temples. The Air Nomads, on the other hand, could have simply flown off the mountains and escaped. The Fire Nation's air ships were not created until much later so, they had no means of pursuing the flying airbenders. Even if some couldn't fly, the Air Nomads still had sky bisons as well. Villain Fire Lord Ozai is among the few firebenders capable at the time of flying using firebending. Imagine an enhanced army not only incapable of defeating a pacifist nation with no army, but many were also defeated by a single monk. That's not a confidence boosting story to tell a nation in pursuit of world domination. But the question remains as to what happened to the Air Nomads if they did survive the Fire Nation's assault.

Avatar: The Last Airbender can be streamed on Paramount Plus.

Just like the dragons, it's possible the Air Nomads either sought refuge elsewhere, some place the Fire Nation could not reach by foot at least, or like Aang during his time of hiding amongst the Fire Nation, the Air Nomads could have lived in exile among the other nations. Unfortunately, the latter option means the culture of the Air Nomads would become threatened to extinction. Using their bending or engaging in cultural practices such as tattooing their members would become a lost art and way of life sacrificed as they would become assimilated into whatever culture they joined. Therefore, the gene or affinity for airbending after a hundred years would be replaced or suppressed with each new generation born to the people of the other nations in Avatar: The Last Airbender.

This could mean that the Fire Nation's propaganda could be both fact and fiction. If true that the Air Nomads fled their temples and received asylum among other nations, such as the Northern Water Tribe or the Earth Kingdom's Ba Sing Se which were both unconquered at the time, then the Fire Nation succeeded in not killing the Air Nomads per se, but rather in extinguishing their culture and community. In that sense, it's more accurate to say Aang was the last practicing airbender by the beginning of the series.

This theory would make the Harmonic Convergence in The Legend of Korra more substantial because it granted, if not randomly, non-benders the ability to airbend. But, another perspective would be that these "non-benders" are airbender descendants who were reconnected with their ancestral heritage to be able to airbend after the Harmonic Convergence. The event may have caused a shift to unsuppress their airbending gene or elemental affinity. Just as the Avatar is connected to their past lives in Avatar: The Last Airbender, this lost airbender tribe may have always been connected to their airbending roots; they just needed a little push.