I wouldn't start over, since you would lose a lot of progress in the game. You can have your kids (if you have any) pick up mushrooms (and if you search the forum you'll find little tricks that can produce more food from them). You should also have all the adults researching any time that there isn't actually any food to gather.
Some of your villagers might die from starvation, but not all of them will, and you'll be able to keep going.
