Evolution Question about the first living organism..?

The first organisms were procharyotes (bacteria).  Bacteria then much like bacteria today reproduce asexually meaning they just split into 2 new cells.  Prior to living organisms, organic molecules were reproducing by themselves (principle of self assembly).  This was the case for a molecule call RNA which has been shown in laboratory experiments to still have this function today.  Asexual reproduction basically evolved from the principle of self assembly; exactly how is still a topic of debate.

Individual molecules will self-replicate on their own by acting like self-templates. Such molecules as RNA and some enzymes have been shown to self replicate in conditions set to simulate conditions on the early Earth.

There would have been no complexities of later cell division - the RNA would simply have inscreased in number inside a simple "bubble" of lipid (a liposome) until it burst the liposome and formed two or more daughter liposomes.

There was therefore no necessity for it to "evolve" any particular mechanism during its life. Evolution does not take place during the life of any organism - evolution takes place between one generation and the next.