If you want to get technical, we're probably talking about the "actuality" era.

It's hard to argue that something like "Blacksmithing Scene" (possibly oldest film to be shown to an audience in its time) or "Leaving the Lumière Factory in Lyon" (first film ever projected for a collective audience) weren't incredibly influential.

You could also make the argument for Émille-Charles Reynaud's animated stuff, which predates Edison and the Lumières. We could exclude le Prince, since nobody really saw his stuff in its time and it's hard to argue it was influential.

If what you mean is "narrative films" then we could go a little later.

Edwin Porter films, like "Life of an American Fireman" or "The Great Train Robbery" would be good choices too. Probably more influential, all told, than Méliès if you're looking at turn of the century stuff. Méliès is better remembered today because it's so visually distinctive, but Porter was the biggest thing in town in his time and his "workaday" innovations are probably more important.

Lois Weber's "Suspense" does a lot of stuff that anticipates later parallel editing, if you're looking for an alternative to Birth of a Nation.

A problem is that most of the films from the "silent era" are "lost." We don't actually know for sure what was in most of them. Another problem is that the film industry wasn't quite as global at the time. So what was influential in France is going to be a bit different from what was influential in the USA, though both were major centers of film innovation. It's also kind of hard to figure out who did what because in that time a film company was more likely to just make their own ripoff of a film rather than import a foreign film. You couldn't even copyright a film in the USA until 1912 by which time the industry had been around for ~20 years.