On my AP US exam this year there was a political cartoon from the Revolutionary period. Instead of speech bubbles, there were "speech scrolls," sort of like what's under a European coat of arms. This got me thinking about the origin of the bubble shape, as it is now pretty much ubiquitous across all comics.
Follow up: when was the first "thought balloon"?
I find a very early example of a speech bubble in a quite well-known caricature of the English civil war. I have wondered before whether anybody has more information on that drawing. Is it authentic?
Apart from that, the earliest modern type of speech bubble I could find was from 1780. James Gillray appears to have helped popularise them. By 1800 they were ubiquitous in English caricature.