A origin implies a past action that originated something. If time didn't exist before the universe , you can't say that something happened before the universe.
"The universe has an origin" would mean it was born from nothingness, which cannot be for nothingness does not even include conditions for anything's appearing. Notice: saying it could be born from something else is fallacious because by "universe" we mean "all that is".
At the quantum level, time does not necessarily always move in one direction, so it's entirely possible that, from our perspective, creation hasn't even started yet.
Observations indicate there was an event in the distant past "the big bang" this is consistent with the universe having an origin. No observations to my knowledge are consistent with it not having an origin.
vic
