How long would it take the Earth to start to recover?
From an asteroid strike/super volcano eruption? In the film it seems about a decade since the disaster and the Earth is still slowly dying...
The ending is supposed to be happy, but it doesn't seem like there is any kind of future for the boy or the family, even if they don't get killed by a gang.
In the book it's implied the family is likely part of a larger group, maybe part of one of the "communes" that is mentioned. Perhaps a place lucky enough to be using green houses and trying to grow food in a controlled environment. But even that would seem pointless if it would take thousands of years for new growth to start. Canned goods don't last nearly as long as people think. All the canned goods in that bomb shelter would have already be long expired.
I'd imagine perhaps the only people in good shape at the moment were those lucky enough to get to the Mountain House food warehouse.