A fertilized egg is alive in the cell-biology sense. It's a living cell. Sperm and egg cells are alive in exactly the same sense. If we look closely at the human (or any other biological) reproductive process, there's never a single instant in which life is absent.
I think that there's only been one origin of life, seemingly way back in pre-Cambrian times, and life has been spreading into new ecological niches and elaborating continuously since then. (Actually, it's possible that there may have been several early origins of life, but apparently only one lineage has survived down to the present day.)
That implies that the search for the initial origin of life in each new generation is probably misguided, at least from the biological perspective.
But there are several closely related questions that we can ask. Each of them has a rather different answer. Which ones we choose to be definitive in things like abortion law is a matter of taste, I guess.
There's the question of when the new generation's unique genetic individuality begins. The answer to that one seems to be at cell-fertilization. The fertilized egg and all of the cells that it generates by subsequent division are all genetically distinct from the parental generation. That's a brand new genetic individual, but it isn't new life.
There's the question of when a newly forming fetus becomes viable, in the sense of being able to live on its own apart from its mother's womb. That's in late pregnancy sometime.
And there's what might be the most difficult question of them all to answer, when does a new PERSON appear? That's what I sense a lot of respondents to this thread are really thinking about and why they perceive this life question as a philosophical issue as opposed to a biological one. I'm not sure how to answer it, though I'll offer the opinion that personhood is somehow associated with reflexive awareness, with our sense of ourselves as selves. That probably appears at some time in early infancy.
Yes, I can agree with every bit of that. However, the way I took the OPs question to be is "when does NEW life begin." And that takes me back (still) to your very first sentence - which is what I've been saying all along.