  The James Webb Space Telescope (JWST), which has recently become operational,
is capable of detecting objects at record-breaking redshifts, $z \gtrsim 15$.
This is a crucial advance for observational cosmology, as at these redshifts
the differences between alternative cosmological models manifest themselves in
the most obvious way. In recent years, some observational hints have emerged
indicating that the Standard Cosmological Model could require correcting. One
of these hints is related to the discovery of remote galaxies whose redshifts
correspond to the very young Universe (less than one billion years after the
Big Bang) but which are similar to nearby galaxies. The issue is that such
galaxies in the early Universe do not have enough time to evolve into something
similar to the late-Universe galaxies. JWST observations of high-redshift
objects are expected to shed light on the origin of this issue. Here we provide
results on performing the ``angular diameter -- redshift'' cosmological test
for the first JWST observation data. We compare this result with predictions of
the standard $\Lambda$CDM cosmological model and some static cosmological
models, including Zwicky's ``tired-light'' model. The latter is currently
assumed to be ruled out by observations. We challenge this assumption and show
that a static model can provide a natural and straightforward way of solving
the puzzle of the well-evolved galaxies and better agreements with the results
of the JWST ``angular diameter -- redshift'' test at higher redshifts than the
correcting evolution model within the $\Lambda$CDM framework. We discuss
several cosmological tests that will be important for further research on the
possibility of revising the expanding Universe paradigm.
