Let's assume all processes are TPC symmetric. Be it the breaking of an egg (just reverse all momenta of all particles involved), the evolution or collapse of the wavefunction (a big if but let's assume), or the expansion of space.
This means we can't determine by looking at a movie that's played backwards that time is actually going backwards. All processes could actually be going forward with appropriate initial conditions. Though I'm not sure of the effect of dark energy. Could it be turned into contracting energy? But let's assume.
Which brings up the question what actually causes time to go forward when it could go backwards as well. Is it the asymmetry between the begin- and end-state of the universe as a whole? Is it just impossible for the begin conditions to lay at infinity? Are parity and/or charge involved?