[raattgift]

You have the analysis right (incompressibility of phase space), but maybe not the application.

Bbs are arguments against the early low-entropy state of the universe being a fluctuation out of thermal equilibrium, and of a future universe fluctuating out of the approximately de Sitter state of the far future.

Expanding steady state was an effort to capture the increasing evidence (including redshift relations) in favour of a Lemaître-style dense early universe, and to avoid several problems with ~static universes.

Since a steady-state cosmology has neither an early low-entropy configuration nor a late homogeneous equilibrium state (steady-state means homogeneity & isotropy in time as well as space: the "perfect cosmological principle"), I'm not sure how a BB argument arises in such a model. In an expanding steady-state model, is there some mechanism for making BBs other than to have them appear with the other components of new gas which under self-gravitation fragments into systems with negative heat capacity?