Purchasing a burger at a busy restaurant in a large city will not affect how many burgers they purchase from their distributor.

It will, by exactly 1 burger. More specifically, if their unit of buying is a box of 100 frozen burgers, and they use the surplus from each day to start the next, then in the long run they will have bought exactly 1 more burger than they would if you had not bought yours: one in 100 of the boxes they get through will have been purchased 1 day earlier than it would have been.

This is a common fallacy: saying that if a large change in X produces a large change in Y, then a small change in X will produce no change at all in Y. Stated like that it's obviously absurd, but in concrete situations people apply the same wrong thinking as you have just done.

Compare the marketing parable (I don't know if the exact scenario ever happened) of the manager at a burger chain who suggested putting just 5 sesame seeds less on every bun. No-one would notice and they'd save money over millions of buns. Repeat until they have no customers left.

Here's another example. You are about to leave home to drive somewhere. There are many junctions with traffic lights on the way, and you will probably have to stop at some of them. If you are delayed by one second leaving home, by how much is your expected arrival time delayed?