The beginning of this speculation is oriented around early life forms, not the origin of life, but rather how simple primitive cells may have begun to evolve.
Therefore one of the initial assumptions is that primitive cells existing during this early period were fundamentally unique. Reproduction was not yet part of the dynamic, and these "cells" were little more than primitive chemical factories, capitalizing on their environment.
One of the first questions to surface is why reproduction would have evolved at all.
If we imagine that these early life forms were simply moving around, acquiring resources from their environment, there is no apparent reason why reproducing should be necessary or even desirable. After all, producing offspring would simply increase the level of competition for the original organism. The downside, of course, is that any organism that died would have no future representation. However, it's not immediately apparent why this should be a concern. It would simply be a slightly different form of extinction, but there's no reason to presume that such primitive cells were anything but immortal, for all practical purposes.
From this we can readily speculate that all manner of possible lifeforms existed, since any conceivable configuration might be successful within this context.
So, the issue of reproduction becomes an important consideration because there doesn't appear to be any benefit to an organism in doing so. As already mentioned, it simply increases competition for the same resources, and consumes more energy on the part of the organism to achieve. After all, if all the resources one needs are readily available, then why not simply float about [or whatever it is that they did] and keep everything for yourself?
My own speculation suggests that the first act of reproduction was largely an accident. Perhaps a cell broke or divided in some uncontrolled fashion, but managed to retain a sufficient amount of its internal chemistry to be relatively evenly split.
It is entirely conceivable to imagine that such early offspring may well have served as food, but perhaps there were enough free resources to where such predation wasn't even a part of the landscape yet.
At this point, by increasing the level of competition, it also increased the competition for resources to all other organisms in the vicinity. As a result, even without any sense of cooperating, this would invariably create a minimally two against one dynamic for any organism encountered.
From this it is conceivable that there may have been one or more organisms that had a greater propensity for such splits, which would invariably out-compete organisms that didn't reproduce. However, it would also be expected during these early stages that reproduction was a quite haphazard affair.
Perhaps it was this kind of situation that gave rise to chemically recording the constituents that made up the organism, so that a copy of that information could be provided to the newly divided half. This could have been an early precursor to RNA/DNA. In other words, the role of RNA/DNA would have been to record what had worked in the past, and use those structures to maintain that "information" into future generations. The means of passing this information might have been an early version of Horizontal Gene Transfer (HGT).
At this point, all new organisms would have the "knowledge" of their shared history and could avoid the riskiness of having to discover things for themselves.
Of course, once we have multiple organisms produced by division, it becomes easier to see how various sensory organs might arise to identify each other, so as to avoid wasting energy in pursuing related organisms as food. Obviously such basic recognition is a precondition to avoid undoing everything gained by reproducing.
Similarly if there was some method by which information could be recorded in a form like RNA [which perhaps was little more than a captured virus], then the groundwork would be laid for the evolutionary trajectory that would produce all other lifeforms.
NOTE: Obviously there would be no viruses that represented RNA/DNA configurations, so the use here is rather gratuitous and refers to any long-stranded molecule that might be exploited to more specific purposes.
Science supports the idea that many of our microbial ancestors also exploited others in either symbiotic or commensal relationships, thereby hastening the development of complex organizations and operations that might be prohibitive if they were dependent solely on evolutionary processes. So the capture of bacteria to become mitochondria, or the creation of a membrane around the DNA become various mechanisms employed to segregate the cellular processes and refine the overall behavior producing a more sophisticated means of survival. In short, each new development requires increased complexity and capability because of the high success of predecessors. In other words, to be able to compete with the organisms already present, then newer, more specialized complex organisms would have to evolve to capitalize on those niches that weren't already occupied, or to be better competitors in those niches that had occupants.
In any case, from this point on it becomes easier to see how life may have followed various forms that we're already quite familiar with, so this becomes less speculative.
However, just for the fun of it, it is interesting to consider what events may have occurred to cause organisms to take that first step towards reproduction. After all, without reproduction there is no need to convey information into the future, so RNA/DNA are irrelevant until that fundamental question is answered.
Anyway ... I'm hoping others may have some interesting speculations about this issue.
For an interesting review of life's origins: