What I can tell you being a history buff is that putting meat between hunks of bread or rolls is not new. Its thinking on your feet food 'traveling food' and just about every culture that bakes bread and eats meat has a 'sandwich' on their list of favorite foods.
Basically, it is traveling food. It makes sense to eat a sandwich when you are traveling or commuting. The world of work makes demands on us. So, taking and eating a sandwich to/at work is convenient as in time saving and frugal. It can be wrapped up and put in a bag or a lunch box. Whether you make it yourself or order it, the sandwich is a main stay and here to stay.
Here are some of my favorites: