Entropy is not due to the equations of our universe, but rather the initial conditions. So the asymmetry might be apparent but the equations might still be symmetric. Related is the idea of spontaneous symmetry breaking.
Of course, we don't have time symmetry in the equations anyway because of the weak force. But because the weak force is weak//doesn't matter much for the physics of many systems, we can often write the equations of physics as a time-symmetric term which essentially decides the motion plus a very small time-asymmetric term. So we can deal with the small term using techniques like perturbation theory, and use time symmetry for the rest.
Of course, we don't have time symmetry in the equations anyway because of the weak force. But because the weak force is weak//doesn't matter much for the physics of many systems, we can often write the equations of physics as a time-symmetric term which essentially decides the motion plus a very small time-asymmetric term. So we can deal with the small term using techniques like perturbation theory, and use time symmetry for the rest.