If you live long enough, you may eventually live past the point where science makes it possible to live forever. For most of us, this is impossible because we lost the birth date lottery.

We don't currently have the means to live forever, but if you manage to live long enough, you might survive until we do.

You just have to live long enough for some new technology to appear to give you the extra years you need to wait for the next new technology.

Even if at no point actual immortality is developed, you can go like this forever, finite life extension by finite life extension.

If technological progress continues exponentially (including increases in human or machine intelligence to make them possible) then our understanding of biology and life-extension will continue to increase, and many such life prolonging-treatments will be made available to the public.

If one life extension makes you live 5 years longer, and during that time an new one comes out that lengthens your life by a few more years, you can see how one might keep "catching" these just in time and thus gradually transition from mortal to immortal.