Random mutations causing cervical cancer essentially does not happen - as a sibling commenter writes, well-studied cases of this are so rare that they’re below our sensitivity of detection/technical error rates.
This is what I mean when I say we try to apply our intuitions to medicine - they’re not reliable and the truth is idiosyncratic.
Because our prior for cervical cancer being caused by HPV is so incredibly high, we would require overwhelming evidence to reject the hypothesis that any new case is due to HPV. There are ways to do this, and, should they be attained, would be published in a reputable journal based on their novelty.