We know he wasn't, and that is not really the history of it either, although most people seems to think it is.

The concept of two slices of bread with something (mostly protein) inside them goes as far back as bread does. But it was mostly used by working people who needed a portable meal that didn't easily spoil. So in the time of the Earl of Sandwich it was farm hands, shepards and so on.

He just used that method and made it fashionable amongst the wealthy, and then it trickled back down to the middle classes, who now saw it is a socially acceptable form of meal.