What about the universal constant-the speed of light?
From what I've read, in inflation models, it's space itself which is coming into existence, hence the speed of light isn't a barrier. Stuff moving in space appears to be unable to exceed light's speed, but the expansion of space itself can.
Not just space, but space-time altogether is coming into existence. The early universe did not 'travel' anywhere. It stretched out like a balloon or a bubble and light stretched out with it.