I agree that it hasn’t been demonstrated as a certainty; however whether it is a “likely” event is a rather normative consideration, wouldn’t you agree?
The gap beween the largest known stable organic molecule (not produced by life already existing) and the smallest known replicator is huge.
What does size have to do with it? Some self-replicating RNAs are only a few hundred base-pairs long. Additionally, what do we mean by “stable”? Stability is a function of environment as well as the specific structure of the molecule in question. One major cause of instability in the present environment is molecular oxygen. Since molecular oxygen is effectively a product of life (it is so reactive that unless it is constantly replenished in the environment it disappears all-but completely) when we are discussing the origin of life we are talking about an anoxic environment. That is important because anoxic environments favor reactions like the polymerization of nucleotide bases.
If this range is continuous with all or most of the intermediate molecules being stable, it would have been easy to demonstrate the emergence of a replicator in the laboratory by simulating the conditions for the formation of each of the intermediate molecules in succession.
We’ve identified several environments in the early Earth where many molecules of biological relevance would have naturally formed and polymerized. We’ve also taken those materials and made self-replicating molecules from them. I don’t see how that doesn’t satisfy the conditions you’ve set here.
However, that is not the case. One way to explain it would be that we have no yet discovered the intermediate stable molecules and the path to to the first replicator. Another way would be that the conditions changed so rapidly that stability was not so important as possibility of the next complex molecule forming, which makes the emergence of the first replicator an extremely unlikely event that happened. That is probably what someone means when (s)he says life happened by “chance”.
Since I disagree with the first part of this paragraph, the last sentence is still unclear.