What would happen if fast food never existed?
Fast food has existed as long as there have been places where one could exchange a good or service for food.
One of the things discovered in the buried city of Pompeii is that there were whorehouses and fast food joints. That's because at the time of the eruption that buried the city, Pompeii was a seaport. It isn't, because seaports can become inland over time due to river silting.
It is not known if Adam and Eve encountered Golden Arches on their journey away from the Garden of Eden, but there might have been something like that.
You would probably have to go back thousands of years to wipe fast food out of history, since Romans used to have little fast food places. Fast food is not necessarily bad food, it's just food whose nutritional value is secondary to it's convenience value.
If you mean large national fast food chains as made popular by America, well then I think we would simply have more little restaurants in their place like other countries do. Instead of ten McDonalds franchises, we would have a little taco stand and a little pasta joint and a cozy pizza place, etc. Actually that sounds really nice.