Samuel Pepys is one historical figure who can be diagnosed with PTSD, according to a publicatioin by Irish professor of psychiatry R. J. Daly in the British Journal of Psychiatry in 1983.

"The Diary of Samuel Pepys" includes a vivid description of the Great Fire of London in 1666. Pepys describes the mounting horror of the fire, and his words reveal evidence of what would now be called PTSD. As a witness to the Great Fire, Pepys personalizes the threat. During the fire, due to stress, he begins to forget events throughout the day, and inserts some details afterward in the margin of his diary. Afterward, he sufferes insomnia, and then anxiety. He has nightmares for about eight months. There is also anger at authority, similar to the anger some modern vets display. Pepys doesn’t write down a remedy for his condition. He doesn’t even seem to notice that he has a condition, although he does describe the suicides of other Londoners after the fire.

The Pepys' diary tells us that the distress a person experienced 400 years ago follows similar pattern to today's diagnosed "trauma".

And all this is what happened to us and what we saw and beheld. What we suffered in cause for tears and sorrow. The water we drank was salt. Adobe bricks [dipped in] a well were an exclusive possession, guarded under a shield. If some tried to toast something, [it had to be guarded] with a shield. We ate colorín wood, grass from the salt flats, adobe, lizards, mice, things full of dust. We fought over eating worms...

And we had a price. There was a price for a youth, a priest, a maiden, or a little child. The price for any ordinary person was just two handfuls of shelled maize. Ten cakes of water flies or twenty of grass from the salt flats was our price. Gold, greenstones, tribute cloth, plumes, and all precious things were considered as nothing and just spilled on the ground.

That's from the Annals of Tlatelolco, which may have been written as early as 1528 CE, recording the conditions towards the 3 month siege of Tenochtitlan, which had been preceded by months of war, itself had been preceded by a smallpox epidemic which may have killed almost half of the population. It is one of the more poignant passages in the Nahuatl accounts of that time period, showing the deprivation and desperation which manifested in a city cut off from food and water, surrounded by enemies.

Yet, within a few years of that event -- even as that account may have been being written -- a normalcy had returned to society, even as indigenous culture and population continued to be less acutely brutalized (See: Kellogg 2005, Lockhart 1992, and to a lesser extent Leon-Portilla 1992 [eng trans.]). The population adapted and even began to exploit newly imported religious and judicial regimes to their advantage. Society had been broken, but it reformed quickly, with remarkable resilience.

There's really no way to answer your question without touching on modern research, because you are projecting backwards a modern diagnosis which is irrespective of the unique conditions and circumstances of past societies. We simply cannot know the prevalence of PTSD in pre-modern societies with any clinical assurance on account of the diagnostic limitations inherent to psychological disorders. Drawing on the modern data, we do see, however, that most people exposed to traumatic events will not show clinically evident PTSD. Just for example, the seminal paper by Rothbaum et al. (1992) found that women who had been raped almost all qualified for a diagnosis of PTSD immediately after the event, but that number rapidly decreased in the seceding months. De Jong et al. (2001) examined the prevalence of PTSD in four areas which had (withing the lifetime of the sample population) experienced traumatic events. Even in areas where traumatic events were ubiquitous, the prevalence of diagnosable PTSD was in the minority.

Now, you may be asking yourself what this has to do with your question about what were the "mechanisms in these societies that allowed people to deal with these hardships more easily?" The underlying problem of that question is that we do not know now what are the most effective or preventative mechanisms for coping with hardships which may lead to PTSD. Take a look at de Jong paper, it explicitly looked at variables such as age at time of trauma, underlying mental health, presence of torture, death of family, domestic stress, and condition of refugee camps as factors which could determine incidence of PTSD. Or take a look at Ahern et al. (2004) with regards to PTSD in Kosovo, the underlying factors are similarly complex and multifactorial. And this does not even address that there may be a genetic component as well.

The simple fact is that, since we have currently have robust, but not absolutely predictive models, for PTSD today, we cannot reasonably project into the past with regards to which factors would have been significant. Even more, the idea that the myriad proximate interactions a person or persons who had experienced a mass traumatic event could be universalized is complicated by the personal nature of those events. The one prevailing theme in looking at PTSD now which can extrapolated back into the past is that a stable social environment (close family/friends, integration into the broader socio-economic milieu, avenues for support following traumatic events, etc.) is helpful in preventing or mitigating PTSD, but not always. There is no reason to believe that people in the past were any different in this respect.