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I have heard it argued that life as we know it (DNA-, RNA- and protein-based) could not have evolved without the ozone layer to protect it from UV radiations.
It seems to me that mechanisms to deal with this would have evolved. Is there any scientific evidence on this point?
Preamble
The original question asked about fair assumptions, but addressed conviction rather than scientific evidence. This site primarily exists to address biological questions that can be answered or at least approached objectively. It certainly does not exit to rehearse people for arguments against those who have already made up their minds on a topic because of religious convictions. So I changed the question to restrict it to UV-resistance of living organisms.
Answer
It is already known that organisms currently exist that are resistant to ultraviolet radiation. The bacterium, Deinococcus radiodurans, an extremophile which is also resistant to other radiation, is a prime example.
In addition, organisms, including higher organisms, have mechanisms for repairing DNA damaged by ultraviolet light, as summarized in this brief Nature Scitable article.
Hence, even without knowing that the ozone layer postdated the origin of life by a billion years (as @canadianer pointed out), there is ample evidence that life would have managed to deal with ultraviolet light.
