We want ML to predict which marketing campaigns drive product sales. Can it work, and is it worth building now?

The first thing I check is whether the data actually exists and is reliable, before even the business metric it moves. In a case like this I'd start with EDA, because if you can't trace campaigns to products, there's nothing to model. When I hit that, we repaired the links, but we still had to wait until we had new reliable data before building.

After that I'd look at whether a simple rule would do, and who will actually use the output.