Personally I’ve got enough food stored at home to survive the initial phase but if not I’d probably rather try to raid abandoned private homes instead of heading to the closest grocery store. I believe it’s wise to avoid hotspots like that especially in the beginning.
Places like that are generally considered one of the most dangerous locations to go to because so many others have the same idea. Desperate people are even more dangerous than zombies. Stores, malls and gas stations are probably the number one hotspots during the first months.
Depends on the initial level of fatalities.