A national origin myth like Romulus and Remus? No. Religious creation myths? Yes and they're important as hecc because MSR is basically a multi-theocracy.
There are five main religious groups in MSR: Upper Amasarians, Sand Amasarians, Gurás, Christians and the People of the Mountains. Both amasarians share the same creation myth, and I'm not gonna tell it just yet because I'm working on an interesting way to describe it for a factbook. It's coming soon, I promise...
For Gurás, the universe was originally a void inhabited by a single butterfly. The butterfly fell asleep and dreamt of a god. The god then created the oceans, and the butterfly dreamt of islands. The god created humans and the butterfly dreamt of animals. The god created mountains and the butterfly dreamt of lakes and so on. Basically, the whole world is happening inside a butterfly's dream, and will end when it wakes up. Please don't think too much about the lovercraftian implications of that. Also, that's why the flag of Gura and Matos has a bunch of butterflies and a little green guy (the god). This is also why, in the autonomous province of Gura and Matos, interrupting someone's sleep is seen as a hell of a dick move. Dreams are basically sacred.
For the Mountain People, the universe is basically a continuous cycle, being created, destroyed and re-created throughout millenia. The world didin't quite "begin" at any specific point, but rather has been going since forever and will continue going until forever. This idea of cycles influences basically every aspect of the Mountain People's lives, and, of course, they believe in reincarnation.
For the christians, I think you know how it goes.