Without the ability to create their own fire, the Firebenders (or, at least, the most powerful ones) had to learn to summon the magma from the very core of the planet. With this power, they were able to take over the world by flooding town after town with molten lava (as well as the fires that they create). Additionally, they're also capable of erupting and then controlling volcanoes- specifically, supervolcanoes, which literally have the potential to wipe out the entire human species. Given all these powers, it's easy to understand how Firebenders were able to get the other nations to surrender.