[mr_toad]

But a distant observer could also make the same measurement of the CMW background and see themselves at rest. And yet we could be moving away from either other at relativistic velocities, due to the expansion of the universe.

Due to this relative motion we will see different ordering of events at different locations, despite both being at rest relative to the CMW background, so we can’t really say there is a global timeline.

The thing is that the CMW background isn’t global, we don’t see the same background as a distant observer. CMW photons that are passing us now will take time to reach a distant observer, and vice versa.