  We present a physics model for a time-symmetric Milne-like universe. The
model is based on the $q$-theory approach to the cosmological constant problem,
supplemented by an assumed vacuum-matter energy exchange possibly due to
quantum-dissipative effects. Without fine-tuning of the initial vacuum energy
density, we obtain a harmless big bang singularity (with finite values of the
Ricci and Kretschmann curvature scalars) and attractor behavior towards
Minkowski spacetime. The time-symmetric spacetime manifold of our model may
provide the proper setting for a possible CPT-symmetric universe.
