A more interesting paper is Life Before Earth, https://arxiv.org/abs/1304.3381, analyzing biological complexity and projecting into the past for an origin of 9.7 billion years ago.
Life Before Earth
Alexei A. Sharov, Richard Gordon
2013 · arXiv
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From the abstract
An extrapolation of the genetic complexity of organisms to earlier times suggests that life began before the Earth was formed. Life may have started from systems with single heritable elements that are functionally equivalent to a nucleotide. The genetic complexity, roughly measured by the number of non-redundant functional nucleotides, is expected to have grown exponentially due to several positive feedback factors: gene cooperation, duplication of genes with their subsequent specialization, and emergence of novel functional niches associated with existing genes. Linear regression of genetic complexity on a log scale extrapolated back to just one base pair suggests the time of the origin of life 9.7 billion years ago. This cosmic time scale for the evolution of life has important consequences: life took ca. 5 billion years to reach the complexity of bacteria; the environments in which life originated and evolved to the prokaryote stage may have been quite different from those envisaged on Earth; there was no intelligent life in our universe prior to the origin of Earth, thus Earth could not have been deliberately seeded with life by intelligent aliens; Earth was seeded by panspermia; experimental replication of the origin of life from scratch may have to emulate many cumulative rare events; and the Drake equation for guesstimating the number of civilizations in the universe is likely wrong, as intelligent life has just begun appearing in our universe. Evolution of advanced organisms has accelerated via development of additional information-processing systems: epigenetic memory, primitive mind, multicellular brain, language, books, computers, and Internet. As a result the doubling time of complexity has reached ca. 20 years. Finally, we discuss the issue of the predicted technological singularity and give a biosemiotics perspective on the increase of complexity.
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Backtrapolating the rate of increase of complexity of life over time suggests "intelligent life has just begun appearing in our universe". https://arxiv.org/abs/1304.3381
Even if there was heavy bombardment, it wouldn't be everywhere at once, and deep sea vents would be somewhat protected by kilometers of water. (assuming the bombardment wasn't so severe as to vapourise the ocean). That life was present as soon as earth was hospitable fits with the intriguing theory that extrapolates the origin of life to predate earth, based on the rate of increase in complexity: http://www.davidyerle.com/where-are-the-aliens/ (actual article pdf 287kb: https://arxiv.org/pdf/1304.3381)
(not OP) Another clarification: before you said "non-earth life". Panspermia[1] implies Ceres and Earth life are related, so that native Ceres life is hard to distinguish from Earth's (and arguably is the same as Earth life). 1. Backtrapolating exponential evolution finds an origin older than Earth. https://arxiv.org/abs/1304.3381
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