Cancer is when cells overgrow due to mutations in genes that affect the cell cycle, so cells start to reproduce and replicate without the controls. Control mechanisms within the cell cycle usually detect and repair bad DNA, and they make sure the cell doesn't reproduce at too high a rate, and they make sure that cells die at the right time.

Sometimes people are born with an inherited mutation that may contribute to cancer, but about 90% of cancers are caused by mutations that arise in the individual during their life. There's nothing from looking at a mutation to say what caused it, unless they look at your family members and decide that it was an inherited mutation.

The way they decide some chemicals are carcinogenic is that exposure to them correlates with higher rates of some kind of cancer. But they can't look at the mutation itself and say what caused it.

If you get a type of cancer that they have already noticed is highly correlated with exposure to a chemical you work with, then they might be able to say that your mutation was probably caused by that chemical.