Buy a big package of hamburger buns and put it in the freezer if you must; it'll be fine for a while there. Thaw as you go when you want a burger: bread thaws in no time. Buy a large package of ground beef, super cheap, and segment it, re-wrap it, freeze it in amounts you know you will use when it is thawed. Want a burg? Water-thaw the meat, air-thaw the bun. Pickles are pickles and are always ready. Pre-made condiments last forever. Pull from your evolving collection of veggies OR make sure you swiped some toms and lettuce or whatever on your way home along with other ingredients for further meals because that's called planning ahead.
There, cheapest burgers you can possibly have, and better than fankenfood. It's just... organization.
Can a particular fast food meal be cheaper than some similar grocery store meal? Yes.
Is a fast food meal cheaper that the maximum cheapness calories per dollar than everything you can get at a grocery store? No.
Will people who hear it hear the second or the first?
Definitely unambiguously the first unless they're the ones trying to "well acshually" it. At the point of the second you're not even talking about burgers - the maximum cheapness calories per dollar is a five gallon jug of corn syrup or something.
It boggles my mind anyone can think that fast food is cheaper than grocery store food for the dollar. Its basically on the level of flat earthers to me.