No, tracing back the steps of gradual change across generations could potentially lead us to the first lifeform i.e. the first common ancestor. However the ToE can't describe the transition from non-life to life since, as others have pointed out, the ToE is the change in allele frequency in species over time. In other words for the ToE to function there must be transmissible genetic material e.g. DNA or RNA.
Now I've never kept up to date on abiogenesis research, so I'm just going to remark on two examples I can remember off hand: the polymerisation of RNA and the formation of phospholipid bilayers. It has been shown that clays will catalyse the formation of RNA polymers, potentially giving rise to short-chain RNAs with biological activity. This is important since its found throughout modern cells (mRNA, tRNA, ribosomes), it can replicate, catalyse reactions, and may have been a precursor to DNA-based life. Phospholipid bilayers are the main constituent of the membranes of all modern and will form vesicles due to the polar head and non-polar tail of these molecules. You will notice that neither of these processes occur due to transfer of genetic material, so can't be described by the ToE, but is a spontaneous process based on the chemical properties of the molecules involved. Other areas of research include understanding the composition of the early atmosphere, since which molecules will form will depend on if it is oxidising or reducing. I think various metabolic pathways have also been identified which do not require the protein based machinery of modern cells. In other words abiogenesis involves chemistry, not biology.
By the way, you keep on saying you accept the ToE so far (in fact all of it if you didn't conflate it with abiogenesis), for example for speciation, but it would be really helpful if you would identify where you think the ToE stops i.e. can't take it back any further. This would make it a lot easier to discuss the specific issues you have because, after all, there is a huge gulf between the formation of the first life and the speciation of modern organisms. In other words please define a kind. Is it the family level, phyla, domain etc.
Edited by Meddle, : No reason given.
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