Ahh, nah, that's not what the situation was back then. The situation back then was different than what we have today. Imagine more of a lot of complex hydrocarbons (which are one of the most common compounds in the universe), that through various reasons turned into things like amino acids, which eventually became rna, which eventually became self-organized. The thing is that life was not some huge jump that happened at one point. It was this huge slow change, that wasn't "life" one second and then the next was. It took a very. very. very long time, and eventually became something we no would consider life. And even after that, it continued to take a very long time afterwards before distinct cells were formed.
Basically, the chemicals weren't distinct organism all living together, they were just all these complex chemicals there intermingling and interacting, that through sun radiation and whatnot (energy being put into the system), chemically reacted enough times in the right way to push its way in the direction that eventually become organized enough for evolution to start. Before that point, before that, there was no "evolution" in the sense that we know it. Just horizontal gene transfer and chemical reactions.
That was a bit complex, sorry. It's been a while since I've had to explain the basics.