If we imagine a moment in time then we can imagine that it could be described exactly as regards the position and direction and momentum of every particle at that moment. But we now know that there are no discrete 'moments' in time. If we consider a period of one hour, then that period can be artificially divided into minutes and then seconds and then fractions of a second but it makes no sense in reality.
The information that describes a point in time (let's say at 12:30pm as we perceive it) is just a slice through the information that describes the the position and direction and momentum of particles during the hour between 12:00 and 1:00pm.
Consider the information to be three dimensional, describing position, direction and momentum. You can spin that cube any way you want and slice it at any angle at any point and time has no direction. All you can determine is elapsed time.
So it would be literally impossible to say that the conditions at one point (wherever you sliced the information cube) caused or were the result of the conditions at another slice. And as we can only perceive one slice at a time - the present, it seems obvious tonus that there is a past and a future. Hence an arrow of time.
It's like being a 2d flatlander and not being able to envisage a third dimension. It is beyond us. But just like a 2d flatlander could mathematically describe a third dimension (and fourth and fifth etc), we can mathematically describe an existence that has no temporal direction but cannot mentally conceive it.