As someone born in 1994, I cannot say one way or another what will happen by the time I am near my natural death date (around 68-70 years of age, though my relatives have held out for up to 95 years). This is because there are just so many variables.
- Ability to extend lifespan at all. There's a possibility that mammals like us simply can't live indefinite lifespans barring cybernetic upgrades because our bodies are far too complex compared to, say, lobsters or jellyfish.
- Technological ability. Biotechnology is always advancing, but it's still primitive, so both cybernetics and genetic engineering are still a ways off. But when we do develop the ability, will it be enough?
- Age of a generation. Exactly what it says.
- State of society. Feeds back into #2, but there's also the possibility that life-extension/youth restoration is restricted to a certain class, caste, or group of people, or that primitivists or fundamentalists come to power and viciously bar anyone from using the technology. It's also possible that the future is perfectly neo/post-liberal but the world is so fucked up that there's laws to prevent people from our generation from using life extension or youth restoration either out of revenge or because it's too wasteful.
In the end, I still have to say that artificial intelligence is the key to all this. Without AI, aging will be a disease plaguing us for centuries, if not millennia. I can't argue that AGI is what's necessary because we could probably do it with narrow AI. But I'll assume AGI is the basic requirement.
In an optimistic scenario, human civilization suffers no major setbacks and technology keeps on progressing at a healthy or even accelerated pace. Thus, we get AGI sometime in the 2030s or 40s, and human level AGI not much longer afterwards, meaning that escape velocity could be reached by the 2040s.
Now you have to realize what that entails— the first people who would benefit are those from the Silent Generation who still wish to live. Imagine we reached escape velocity today and the oldest living person decides to use biotech for life extension. The current oldest person is 117-year-old Nabi Tajima, born August 4th, 1900. Assuming a creeping advancement year over year with the oldest living person always being 117, the oldest person in 2045 will have been born in 1928. Baby Boomers will still be around, though they'll definitely be dying off en masse— 2045 is the 100th anniversary of the start of the Baby Boomer generation, and it doesn't really fizzle out until you get to 1965, so the youngest Baby Boomers will be 80 years old. Generation X starts around there as well and peters out by 1982 or so (though it's debatable when it actually ends), so the youngest members of Gen X will still be younger than the retirement age. I'm a Millennial, but I'm pushing it, and I'll be 51.
Will was born in 1979, so he'd be a bit older than retirement age— 66. That's still relatively 'young' as far as geriatrics go, so long as he doesn't contract some disease or cancer (which, as possible to expect, might be curable by then).
By the time I'm near my natural death, it will be ~2065. If we haven't developed AGI or life extension tech by then, I'll be very surprised. And that's the lead-in to the pessimistic end of it— something happens between now and 2100 (when the start of Gen Z will be turning 100) that pushes life-extension tech back so critically far that no living person ever gets to use it. Whether that be something like environmental collapse, nuclear war, or an astronomical catastrophe a la asteroid impact.
Or maybe we don't develop AGI because it's genuinely impossible or much harder than we ever could have imagined and thus things like cybernetic augmentations or advanced genetic engineering progress exponentially for a time before slowing to a linear and incremental growth. Or we prove something about biological aging that makes life extension orders of magnitude more difficult to solve, meaning that even if we did have AGI it'd take many decades to reach escape velocity.
It's possible that there's a maximum lifespan for every mammal, so without biotechnology, even all the medical tech we have won't prolong our lives. Some suggest this may be 125 or 130.
But once we reach the point where life extension is possible, that's it. Because now a person who would have died at 115 will instead die at 180, but by the time they reach that age, technology has progressed much further so that their lifespan could be 400 years, and so on and so on.