In addition to the U-238 and U-235, there is also radioactive Thorium 232 still around that was in greater concentrations 4 billion years ago (14-billion year half life). And, there may well have been more isotopes that are completely gone, or almost so, by now, such as PU-244. We really don't know how much of various radioactive materials were created by supernovas to seed our solar nebula/planet forming disk and what their abundances were 4.3 billion years ago.
Also, there is no reason to assume that all the local concentrations on Earth were near the average value for the crust. Uranium accumulated in Oklo, probably in a wet environment, to a sufficient degree to create a "natural reactor" where fissions induced more fissions, but at a "subcritical" level that didn't "run away" in an exponential manner.
So, speculation about radiation dose rates "where life formed" seem highly subjective and uncertain.
One thing that seems to be certain is that the bacteria that we find today living miles below Earth's surface get their energy from the chemicals that are formed by the ionizing radiation from radioactive materials striking other local materials, creating a chemical energy source for those bacteria to feed on. So, life may well have initiated under ground, where pressures and temperatures are higher than on the surface. Instead of a "warm little pond" on the surface, life might have originated in the underground cavities at the bases of mud volcanoes. Or not. But, if so, it would not require cosmic rays or a hot sun, or even an atmosphere of a particular composition.
Even if we do eventually succeed in a lab with making self-replicating chemicals that seem to have the ability to evolve, that does not necessarily mean that it happened the same way on Earth 4.something billion years ago.