products of an asymmetric reaction performed without enantiomeric control can selectively catalyse the formation of more products with the same handedness -- this is called autocatalysis. so the first full reaction might produce a left-handed product (by chance) but that left-handed product will then cause future products to be preferentially left-handed. see the [Soai reaction](https://en.wikipedia.org/wiki/Soai_reaction?wprov=sfla1) for an example of this.
as mentioned by others this is conjectural but it is a popular (if somewhat unfalsifiable) explanation for homochirality
as mentioned by others this is conjectural but it is a popular (if somewhat unfalsifiable) explanation for homochirality