How long did it take for life to begin and evolve to cyanobacteria?

@article{Lazcano2004HowLD,
  title={How long did it take for life to begin and evolve to cyanobacteria?},
  author={Antonio Lazcano and Stanley L. Miller},
  journal={Journal of Molecular Evolution},
  year={2004},
  volume={39},
  pages={546-554}
}
There is convincing paleontological evidence showing that stromatolite-building phototactic prokaryotes were already in existence 3.5 × 109 years ago. Late accretion impacts may have killed off life on our planet as late as 3.8 × 109 years ago. This leaves only 300 million years to go from the prebiotic soup to the RNA world and to cyanobacteria. However, 300 million years should be more than sufficient time. All known prebiotic reactions take place in geologically rapid time scales, and very… 
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