The other side to this is that given enough time, some civilisation will be oblivious to the rest of the universe. Their visible universe will just be their own galaxy.
If their physics is correct, they will figure it out. We did because we verified that expansion is accelerating even though our physics are incomplete. Until the late 90s, physicists accepted a cosmological constant of 0, which meant no acceleration. Turns out that that was wrong.
It may be possible that they figure it out via Quantum Mechanics because it seems that acceleration of the universe is related to the energy density of a vacuum / empty space. The problem is that they won't be able to empirically verify that I think.
The problem is that at such timescales, the CMB will have shifted sooooooooo much that there’s nothing they will be able to deduce, all light has redshifted to absurd scales, and worst of all, everything will be so far away that light will never reach the galaxy.