But when we apply statistical mechanics to "microscopic" arrangments like a few particles in an idealized rigid box or in a vacuum, there is no arrow of time. The laws of physics themsleves are totally symmetric (CPT theorem), and it is not thought the t-asymmetry of the weak interaction is responsible for the global macroscopic arrow of time. So without some statement of initial/prior conditions, we have no reason to see just the "forward" arrow unless we say something about initial/prior conditions. (Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox)

Are you sure Ergodic theory does the trick? When I hear people like David Albert or Sean Carroll speak, they always make clear you need some kind of initial/prior conditions or else stat mech does not guarantee why we only see the forward arrow of time. If we assume we can reduce all physical process to the behavior of fundamental particles (or fields), and the physical laws that describe the microscopic world are entirely symmetrical (CPT theorem), you get Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox. They say the Past Hypothesis (low entropy big bang prior condition) is necessary to resolve it.

*And the t-assymetry of the weak interaction isn't the reason according to the wikipedia article on time asymmetry - you still need initial conditions. "Time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe. "