I think it's likely that the first life like our kind was only composed of genetic material.
RNA and DNA are prone to replicating themselves (with many errors and not efficiently) in a wide variety of situations. It's way more likely that evolution selected those molecules for efficiency than that some complex life appeared without some transferable data storage.
No they are not able to replicate themselves, in any circumstances.
Obviously, any RNA or DNA molecule can serve as a template for the polymerization of another nucleic acid molecule.
However the polymerization cannot proceed spontaneously. The nucleotides polymerize by condensation, i.e. by releasing water.
It should be obvious that such a reaction cannot be spontaneous when the molecules are already surrounded by water. You need some molecule able to extract the water from the nucleotides, for example an acid anhydride, like ATP.
That anhydride must have also been produced by water extraction and in the water environment you need an energy source for that.
So if you will complete the analysis you will reach the conclusion that you need an existing living being for the replication, no replication can occur otherwise.
Obviously, in a lab you can yourself substitute the role of that living being, by providing adequate supplies of monomers and of energy sources, so you can replicate nucleic acids in abiotic conditions. Nevertheless, that could not happen in natural conditions.
You seem to want life to appear in a likely condition, without some external power source.
Whatever condition there was, it could as well be some extremely rare one, and I really can't imagine how some molecules could start to reproduce without their environment being constantly changed by some external energy flux.
Besides, I'm no expert, but I don't think there were huge amounts of pure water running around on the early Earth. There were so much more stuff to use those hydrogen and oxygen atoms, and Earth's water wasn't all here since the beginning.
RNA and DNA are prone to replicating themselves (with many errors and not efficiently) in a wide variety of situations. It's way more likely that evolution selected those molecules for efficiency than that some complex life appeared without some transferable data storage.