There is nothing indicating that the universe was spinning as it was created. There was no way for such angular momentum to exist.
The different spins (moons, planets, stars, galaxies, clusters of galaxies, superclusters of galaxies) originated as tiny anomolies in the universe very shortly after it began.
There are many well-respected physicists, such as Stephen Hawking, Lawrence Krauss, Sean M. Carroll, Victor Stenger, Michio Kaku, Alan Guth, Robert A.J. Matthews, and Nobel laureate Frank Wilczek, who have created scientific models where the Big Bang and thus the entire universe could arise from nothing but a quantum vacuum fluctuation -- via natural processes.
I know that this doesn't make sense in our Newtonian experience, but it does in the realm of quantum mechanics and relativity. As Nobel laureate physicist Richard Feynman wrote, "The theory of quantum electrodynamics describes nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept nature as she is — absurd."
"To surrender to ignorance and call it God has always been premature, and it remains premature today."
— Isaac Asimov
For more, watch the video at the 1st link - "A Universe From Nothing" by Lawrence Krauss.