Richard S. Sternberg wrote:

If the Universe is infinite and uniform (Condition #1) and not expanding
(Condition #2, which is somewhat duplicative of Condition #1), then the sky
should be infinitely bright at night. No matter how small of a percentage of
the sky is generating the light, if it has been generating that light for an
infinite time from infinite points in space, then the resulting light must
be infinite. Since the sky is dark at night, the Universe cannot be infinite
and uniform unless the proponent offers a different solution to the Paradox.

OTOH, if an infinite non-expanding universe had a roughly uniform finite
energy density at one point in time, it would be rather surprising if it
came to have an infinite energy density at some future time. Therefore
Olbers Paradox tells us next to nothing about the real universe except
that somewhere in it someone did the sums wrong. :-)

If such a universe existed over vast eons of time then clearly there would
need to be a balance between dust and other absorption and stellar
processes emissions and a means to recycle energy between these. The fact
that we don't know about any physics for such processes might have more to
do with the fact that they are inherently less likely to be observed (and
therefore lead to them becoming known physics) than with them not existing.

Ray Tomes