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It's possible because the universe wasn't spinning at the beginning of the Big Bang.
According to George Smoot's book 'Wrinkles in Time', one reason that we do not detect any 'spinning' of the universe is that the initial inflationary period of the universe acted as a 'break' to it's spinning. Just as an ice skater who is spinning really fast will slow down when they spread their arms, the universe would slow down when it 'expanded' in all directions. Instead of just arms slowing down the spin, you would have the matter/energy in the entire universe being 'flung' out to slow down any spin.
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