Forget the religious notion of a soul, and focus on when the baby is genetically unique and complete. That moment is at conception. Conception is the moment of discontinuity and everything else proceeds from there.
Move backwards from birth and look for the moment at which you can say now there is a person who didn’t exist before and that moment is conception. For years after birth a pattern of growth will continue that is simply a continuation of what was happening before birth. In those month the baby has been growing larger, but expanding on structures that were there before. That heart is told to beat by a nervous system that has been developing from the same set of genetic instructions that directs the formation of the rest of the organs. Those organs grow out of cells that began dividing from a single cell. That single cell began dividing only after the sperm and ova were united. Before the moment they united the ova was just potential and the sperm was one of millions. At the moment they are united the cell is completely changed and the potential is fulfilled.
You explained it in far, far fewer words than I did. I just didn’t know how to explain that painful journey to the truth in fewer words.
That is implicitly recognized by liberals in the case of the eggs of bald eagles, but effectively denied in the case of humans.