Hello crowonsnow,
I believe it happens at conception.
But, scientifically, to prove life you don’t need to believe in a soul at all. A sperm cell is a cell originating from a man. It has 23 chromosomes, men create millions of sperm. Obviously not all fertilize an egg. An egg cell has 23 chromosomes, a woman is born with about 400 eggs that she will use up from puberty until menopause. Not all egg cells are destined to be fertilized, obviously.
When the egg and sperm meet, than an entirely new organism is formed, with a genetic code that is unique to the organism. Future traits such as hair color, eye color, gender, height are all determined at the one cell stage.
This isn’t true just for humans, but for all creatures that produce sexually.
I also believe that the soul leaves the body at death. There isn’t any religious test that is administered to see if the soul is still in the body. We trust that death has occurred by physical cues…lack of heart function, lack of brain function, etc.