Nailed it! The one doesn’t infer the other, not that there is evidence for either.
“caused” and “random” are not antonyms. Bulk behaviors can be strictly predictable (thus caused), but with member components predictable only in terms of probability.
Would you take the position that no mutations are random? Never in nature has so much as one mutation ever been random? Is cancer?
If some are random, what would distinguish random from non-random mutations? Is there a test?
But if quantum tunneling is statistically random, isn’t the consequential mutation random?