There might not be a universal frame of reference, but there is a frame of reference that’s useful to measure: the rest frame of the CMB, which also coincides with the rest frame of the Hubble expansion of the Universe. Every galaxy we see has what we call a “peculiar velocity” (or a speed atop the Hubble expansion) of a few hundred to a few thousand km/s, and what we see for ourselves is exactly consistent with that. Our Sun’s peculiar motion of 368 km/s, and our local group’s, of 627 km/s, matches up perfectly with how we understand that all galaxies move through space. Thanks to the effect of the dipole repeller, we now, for the first time, understand how that motion happens for us on every cosmic scale.