How much time does it take for heavy alcohol consumption to lead to cancer?

Decades: but it depends on the kind of cancer, and whether other co-promoters or enhancers (like tobacco, or hepatitis C) are present. The most common alcohol-associated cancers are head and neck cancer, where alcohol doubles or triples risk, smoking increases it eight fold, but the combination increases it 150 times that of non-smokers, non-drinkers; and liver cancer, where hep C contributes as well.