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Microbiologist here (so no cancer expert!)

Some molecules are more stable than others. As you already mentioned, DNA can be damaged by radiation as energy is taken up by the DNA molecule and then it can fall apart or create new bindings.

Long story short, food molecules can (during their metabolism) turn into highly reactive particles that can damage your cells and DNA. Especially oxygen radicals can cause a lot of damage.

There's gotta be a YT video explaining this a bit more in depth.

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>Generally the only carcinogens in food come from the way we cook and or preserve the foods.

Not so. For example, fiddleheads naturally contain the carcinogen ptaquiloside.

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But there is 'only' an increased chance. Studies only have been done among people with occupational hazard. And they are not conclusive about how big the chances are in relation to chronic exposure to PAHs and metabolites.

[Hammond et al. 1976; Lloyd 1971; Mazumdar 1975; Redmond et al. 1972; Redmond and Strobino 1976].

There have been animal studies and epidemiological studies. No one is going to design a trial to expose humans to known carcinogens. So, as you point out, the exact risk increase with exposure is unknown. Some info specifically about dietary exposure

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The way certain foods are cooked can cause carcinogens to form. E.g acrylamide in starchy food. Some foods also contain naturally carcinogenic compounds eg red meat

One other interesting way food can cause cancer is by parasites. There is a raw fish dish known as koi pla in thailand that is linked to the development of cholangiocarcinoma due to the presence of liver flukes in the fish