The Big Bang did not originate as a single ball of matter despite what some popularizers like to describe the situation. The expansion, however, could have had some net angular momentum, however, this would be seen in the cosmic background radiation as a departure from its uniformity in all directions. It would not be seen in the distributions of the rotations of stars, planets and galaxies. These spin directions are dictated by events that influenced the clouds of gas out of which they initially formed, not by any property of the universe as a whole.