I enjoy creative arguments, so I decided to look it up. The theory is that toast originated in Ancient Egypt as a method of preserving bread, since bread left out too long would go stale, hard, inedible, and eventually mold. It also surfaced in Ancient Rome, where the first breads there were toasted by laying them in front of fires on hot stones. It was exceedingly common in ancient cultures, therefore, I feel it would fit the setting.
http://www.todayifoundout.com/index.php/2013/10/history-toast/ <- Source
I will grant to you that Grilled Cheese Sandwiches were not popularized until the early 1920s, however, there are apparently references to them back in Ancient Roman times as well. I wasn't able to chase the source on that, though.
https://recipes.howstuffworks.com/history-of-grilled-cheese.htm