Similarly it is hard to imagine any object that can be purely 2D in nature, because we are biased to perceive the world in 3D. So we think that every object has to be 3D, even the smallest organism, or even atoms. But a 'fake' example of 2D is a tv screen. It gives us an example to imagine 2D. The point I am trying to make is that time is just our perception. To say causality is always tied to time is a bias created by viewing the universe through a 'time' tinted/colored glass.
The point of singularity where gravity is so high that time comes to stand still, but is still present - this is a possibility.
So maybe time just pauses between big bangs and flows at lower density and lower gravitational fields
So is causality—I'm not really sure what your point is.
I am also confused a tad about the point I wanted to make though, lol. Maybe causality and time is perceived differently in higher or other dimensions that we do not perceive as of now in our human level of evolution. So the assumption of causality exists only due to time being present could be something relative to our perceptions and not true
p.s. for the record, Barbour is no clown, but a serious cat -- he is also the guy that wrote "Absolute or Relative Motion / the Discovery of Dynamics" which is a bedrock treatise on Machian ideas in physics