The other question besides whether such a thing is possible is whether it is desirable. Depending on one's viewpoint, one could look at immortal humans as a cosmic cancer. At least the cycle of death and birth limits the harm a bad actor can do. What would you do if your least favorite fascist were also immortal and invulnerable? And I do mean that somewhat rhetorically. It's a messy ethical subject to think about, personally. I kinda prefer life and death.
[1] https://en.wikipedia.org/wiki/Hayflick_limit
[2] https://en.wikipedia.org/wiki/Biological_immortality#Organis...