The cells that make up our bodies all come from that single fertilised egg created at our conception. It divides into 2, 4, 8, 16, etc. None of our cells was ever dead and infused with life. All of our cells were always living because each cell was created by a mother cell dividing into two daughters.
The sperm and ova that became our first cell were also living cells. produced by cell division in our parents. All of our parents' cells were also always alive and multiplied by dividing.
All the cells of every animal, going back into the mists of time originating by one living cell becoming two living cells. Similarly for all plants, fungi, and bacteria too. All cells come from dividing. All cells except the original cells.
We have a pretty good idea of how such cells might have formed, but we don't know for sure. But in any case, everything alive to day, literally every living cell, was produced by cell division. Every living cell, and thus every living thing, is a direct-line descendant of those first living cells. Every living cell is directly related to every other living cell.
Along the way, some of the cells recombined to make more complex cells or formed symbiotic relationships. Combining is as important as division in evolution, though it happens less often.
The lines of living cells, going back to the original cells, are unbroken for at least 3.5 billion years, possibly longer. Each individual cell eventually dies, but the processes of life continue, without interruption. And even if humans manage to wipe themselves out, bacteria will survive literally anything we can do. Some bacteria live in boiling pools of acid, so nothing we do is going to kill them all. Life will continue on earth at least until our sun expands out to become a red giant, engulfing the earth in fire, about 5 billion years from now. But there is a good chance that by then humans will have seeded life on other planets, if only in our solar system. So in all probability, life will go on indefinitely.
The only limit is that life requires an input of energy which can be put to use. And this will have completely run out in our universe by about 10^100 (1 followed by 100 zeros) years from now. Then it's curtains for life in this universe. Until then, however, life goes on.