I think it's safe to say that the jury is still out on this one.
Edit: One reason this is difficult is that you can think of galaxies as having two major contributions to the line-of sight velocity we observe from earth: expansion of the Universe ("Hubble flow") and "peculiar" velocity (motion due to the local gravitational field in which the galaxy lives). The latter velocities are typically a few hundred km/s (or later if the galaxy is in a cluster). NGC 1052 has an observed recession velocity of 1510 km/s (https://ned.ipac.caltech.edu/byname?objname=NGC%201052&hcons...). Assuming a peculiar velocity of 300 km/s, that means the peculiar velocity is on the order of 20% of the total velocity. But we don't know what component of the peculiar velocity is along the line of sight or whether it's positive or negative. So with these numbers it's "hubble flow" velocity could be from 1200 km/s to 1800 km/s. If you naive plug those two recession velocities into a cosmology model (e.g., the latest model derived from Planck observations) the distance range you get is 17.3-26.1 Mpc, or a ~40% uncertainty. So we cannot rely just on the Universe's measured expansion to get a sufficiently reliable distance estimate.
So one must use other techniques to measure distances. They each have their own advantages and disadvantages. In general most distance estimates are build on the "Cosmic distance ladder" and accumulate uncertainty as you move up the ladder: https://en.wikipedia.org/wiki/Cosmic_distance_ladder