There's nothing inherently unsustainable about social security. If FICA tax revenues don't keep up with benefits, benefits can be cut to make up for the shortfall. If you haven't noticed, due to our still-falling life expectancy, we keep having to move armageddon day back. I think there are many in high places that worry insolvency may never come.
It is unsustainable in its current form. Of course you can cut benefits, raise taxes, raise age, etc to extend it for however long it makes sense. But it was designed for an evergrowing number of taxpayers, who'd support those before them due to strength in numbers. But as the tax burden grows, more and more people are going to be against it. I don't expect the majority of Gen Z will ever see a penny of it. I'm not sure I will, either.
If Gen Z never sees a penny from Social Security, it will be because of the loss of political will to protect Social Security as we know it. Which would only happen if this continuing misinformation campaign convinces the younger generations that they will never get anything from the program.
Social security can literally go on for centuries, just fine, as long as there is political will to keep it going.