This doesn't change the situation. Shortly after removing the barrier, some molecules will start moving into the other half. Just reverse all velocities and see

This doesn't change the situation. Shortly after removing the barrier, some molecules will start moving into the other half. Just reverse all velocities and see all the molecules move back into the half they started in. If you go further forward in time, you will eventually see the first collision. But that doesn't really change the situation, reverse the velocities, see the molecules collide in reverse and then move back into their starting halfs. And this never really changes, particles move and collide and this can be reversed, you just have to do this for very, very many particles and collisions. And this is probably chaotic, the tiniest error in any of the positions or velocities will get massively amplified and give you the wrong initial state. But in principle it could be done. And it has to be done on the microscopic level, macroscopic things like concentrations, temperatures, or pressures by definition do not reflect the microscopic states.