It has already been demonstrated that amino acids and other organic molecules which occur importantly in living things can appear spontaneously under conditions which may approximate those existing in the early history of the Earth. A very crucial step in these theories is the occurrence of a self replicating molecule. As you quite correctly point out, natural selection has no meaning until there is reproduction.
Reproduction is one of the basic requirements for life, but there are others.
I think the other main requirement somewhere along the way would be stabilization of that self replication machinery. Yet we can't have life as too stabile either as then there is no room for higher organized life to arise. Interestingly, life appears to dwell on the edge of this fine balance. Nobody knows how many self replicating molecules are possible. DNA happens to be the one all terrestrial life is based on, but it may not be the only molecule that could lead to living organisms.