What is the mechanism for first living organism/s saving their characteristics for the next generation before genetic information had evolved in the genesis of evolution of living organisms?
I believe it doesn't have a true answer. There was no "
first living organism/s" in that there is no clear way of deciding what life actually is. At some fairly arbitrary point self replicating chemical reactions became life. The best way I can think of to explain that is to ask at what point does a single tree become a forest of trees? Or when does a town become a city, or when does a child become an adult? We cannot give a precise moment because the concept itself is undefinable.
We can obviously see life as much as we can recognize a forest, city, or an adult. We can also assign various criteria for such things, but they aren't real; we just made them up to help us make sense of the world.
There is no good answer to your question Buzsaw because what we call life is just a majority vote. There are several examples of what could be life but is missing one or another criteria, its life... but its not. So if Abiogenesis is true there would not be a recognizable "
genesis of evolution" but a series of steps with a grey area that is life but not life. Or not life but behaves like life more so than a chemical reaction.