My understanding is that DNA can only replicate itself as part of a living cell - it is not living by itself but the key component to the reproduction of cells - which is necessary for our ongoing living.
Dawkins' book, The Genetic Book of the Dead: A Darwinian Reverie, just published September 17, 2024, is very likely to provide as much as scientists know today. I have only just started the book so I cannot yet say how detailed Dawkins is about the evolution of the DNA structure. However, based...