Is it possible that self replication was ignited at the time of heavy bombardment? It's really strange how origin of Life on Earth is correlated with this time.

Is it possible that self replication was ignited at the time of heavy bombardment? It's really strange how origin of Life on Earth is correlated with this time. One possibility might be that our planet was covered with ice at this time while constant bombardment should produce a lot of phase shifts and randomness, contributing to significant recombinations of available molecules in water. It's a kind of top-down approach.