Genetic evolution presupposes the capability for reproduction.
A better timeframe is how long it took to get from the first simple autocatalytic sets to the first replictor. The oldest known terrestrial rocks date back c. 3.8 billion years, near the end of the late heavy bombardment. This gives a relatively small upper bound of 300 million years for reproducing DNA to have emerged from autocatalytic sets of simple amino and nucleic acids, sugars, lipids, etc. Their Platonic metabolisms can repair themselves and propagate through time. Catalysts work by reducing the energy hump chemicals need to climb in order to react.