My guess is that you're wildly overestimating the average 1950s standard of living. In many ways, lower-income folks have better lives today than even the wealthy did back then. You talk about healthcare, but healthcare in the 1950s was practically non-existent by modern standards. You can choose to live in a low cost-of-living area and your $62k will stretch a lot further than in any city "neighborhood".
I probably am overestimating the average 1950s standard of living. But I'd argue you're also overestimating how far $62k could take a family of 5 in CA. Even in the poorest of neighborhoods, far outside of city centers (where you probably wouldn't even be making $62k btw)... even then... I highly doubt you could support a family of 5, and I can guarantee that you would not be buying a house.
I maintain that both of these things were (generally) more accessible in the 1950s.
The average salary in CA is ~62k a year. To support a family of 4 (wife + 3 kids) you would need WAY more than $62k.
Even if you lived in the poorest neighborhood, and never bought frivolous things, you could still never support a family on that salary, and forget about buying a house.
In the 1950s you could support a family, buy a house, pay for healthcare, etc. It seems far more plausible to me that the purchasing power domestically of the dollar was effectively halved at some point in history.