Looking at current aging research, there's a good possibility we'll see rejuvenation in the next decade or two and it'll profoundly change our society. In 20 years, everyone will be looking 25 years old and pointing at frail people with wrinkly faces and laughing, same way we do today with antivaxxers.
Once that's out of the way, we'll eventually get comfortable with building arbitrarily large objects on orbit, and we could as well build a huge spaceship with an onboard self-sustaining ecosystem and fly that to other stars, the boring way. Yes, it will be a very long journey, but it's possible without the reliance on yet to be discovered new physics.