Usually not. There are some cancers that are very linked to occupational or specific exposures (mesothelioma in people exposed to friable asbestos, for example).

The links between most cancers and environmental or behavioral exposures (like smoking or other chemical exposures) are determined statistically by epidemiologists, who observe higher incidence of the cancer in a group of people exposed to a certain thing. These higher rates of cancers have to be 'real' - that is, not just due to random chance. Epidemiologists use statistical methods to show this, and their data covers entire populations, not individual people.

Part of the reason a doctor can't usually tell someone what caused their individual cancer is that people vary. There are lifetime smokers who never get lung cancer and people who have never smoked who do. Cancer in general appears to be caused by a complex interaction between a person's genes, their exposures, time, etc.