if expansion is inferred by redshift, what other evidence do they have to corroborate?
as redshift can be caused by time dilation or means other than motion
One could argue that redshift tells us only about how the light was affected on its journey — stretched due to past conditions of the universe (e.g. a rapid early expansion or initial velocity), but not necessarily because the universe is still expanding today. The mainstream interpretation (ΛCDM model) treats redshift as resulting from the continuous stretching of space during the entire light path — i.e., a photon’s wavelength increases not just from a single event, but as the universe expands throughout the photon's journey. This implies that space is still expanding right now. I would say that the problem lies with the ΛCDM model. Modern cosmologists are bending data to try and follow their model, which as it turns out does not have much if any empirical support.
If we consider the present-day radius of the Universe to be approximately 46 billion light-years, cosmic expansion would mean that the distance between objects should be increasing over time. For instance, in a Universe with a radius of 1.3 × 10²³ km (approximately 13.8 billion light-years), a galaxy or star that is 100 million light-years distant would, due to the scale factor of expansion, now be approximately 333 million light-years away. This suggests that, if cosmic expansion were truly affecting distances, we should see galaxies and stars appearing much farther apart than previously thought. However, this increased distance isn’t immediately reflected in our measurements, possibly due to the way we measure cosmic distances, the limitations of observational tools, or the fact that it is space itself that is stretching. And just how much sense does that make?
The cosmic expansion model, along with the concept of dark energy, largely depends on the Cosmic Microwave Background (CMB) and its estimated redshift of z = 10, which is thought to represent the early Universe. However, the CMB has increasingly been shown to be (Augmented Newtonian Dynamics Theory) more of a reflection of the present-day composition of the Universe, rather than a snapshot of a distant, early cosmic past. The fact that the CMB is remarkably consistent across the sky, with very little variation, challenges the idea of ongoing cosmic expansion. If the Universe were still expanding at an accelerating rate, we would expect to see more significant changes in the CMB's temperature and distribution, (given that it is a present day phenomenon) which should reflect the dynamics of cosmic inflation and expansion over time. The unchanging nature of the CMB instead suggests that the assumptions tied to the standard expansion model may need to be reconsidered, or that expansion, as we understand it, may not be driving the cosmic phenomena as currently theorized.