I think storable food predates agriculture. Nuts keep quite well for very extended periods of time. Smoking and drying fish appears to also have been known for many thousands of years.

The problem with raiding before the domestication of the horse is that it's a lot of risk for not a lot of reward. How much can you carry on your back? Maybe you can carry more on some sort of wheel-barrow, but the wheel was invented after the domestication of the horse (for quite obvious reasons).

Still, while the horse is thought to have been domesticated around 3500 BC, there were fortified settlements before 4000 BC, a sign that raiding or even warfare was common. Sheep and goats were domesticated already at the time, and cheese was known. Maybe raiders were trying to steal cheese? Otherwise, there were luxury items, or status items, like polished maces, glazed and painted pottery, adornments made of animal teeth, and early artifacts made from copper. But I'm not sure it ever made sense to risk your life and raid a village just to run away with a bag of wheat.