That's silly - your DNA is constantly being damaged by chemical means, mostly oxygen free radicals produced in your own cells.

All DNA-based life has elaborate checking and repair mechanisms, that can be upregulated in response to an increase in the threat.

That's why Chernobyl is a beautiful wilderness with the highest level of biodiversity in Europe (but the first few weeks were very destructive).

And why residents in Guarapari have a longer life expectancy than other Brazilians, despite regularly exceeding the maximum radiation exposure the USA permits for nuclear plant workers. (Their rates of neoplasms inc solid cancers are 8% higher, but cardiovascular disease notably lower.)

Humans and other eukaryotes can and do adapt to levels of background radiation much greater than anywhere on Earth's surface in the present day. Radiation doses below this adapted threshold are negligible in their potential for net harm.

Sudden, acute exposure to ionising radiation IS harmful and DOES increase risk of cancer. It is unclear if this increase in risk is linear, but probably not.