Lets be entirely clear that the food crisis in Gaza is manufactured. There is enough food and medicines available and there are several organizations capable of dealing with the logistics of handling out the food, main one among them of course being UNWRA.
The only reason there is starvation in Gaza is because IDF is preventing aid from entering the territory and are refusing to let real humanitarian organizations work safely there.
So the answer to the question is: Israel must let food trucks into Gaza and let serious humanitarian organizations with decades of experience handle the logistics of handing out the food. About 150-200 trucks needs to enter Gaza per day, that's a lot of trucks to inspect thoroughly, but not nearly infeasible.