Perhaps what you're missing, is the idea that moisture and heat combined in a medium of slightly acidic elements such as soil, crushed minerals and lava rocks is all that might be required for simple organic life-forms to begin spontaneously. The earth would have had certain similar conditions over vast areas, which would mean that the first types of life could have begun in the same time window.
Evolution over millions of years has seen to it that life proliferated everywhere, in, on, under and above earth and ocean and it would be almost impossible to differentiate between simple life-forms that have evolved from the beginning without too much mutation and which are therefore still simple, and others that are propagated from scratch in places where there is a major shift in conditions. However, I am of the opinion that the earth continues to bring forth brand new micro-organisms spontaneously where conditions are conducive to it.
