Given there has been something where a big-bang origin of our evolutionary cosmos took place: What is the relativistic line element describing the energy density and pressure of such a pre-existing universal background? The simplest conceivable ansatz leads to a Stationary-Universe Model (SUM), which instead of the 'Steady-state Theory' is shown to be an arguable alternative to the Cosmological Concordance Model (CCM) commonly accepted today. The SUM stands out with redshift values statistically independent of time; a significant Hubble parameter is proved in contrast to the conventional one. It requires a negative gravitational 'dark' pressure of -1/3 the critical density. Intrinsic limitations of proper length and time are derived, which cause a struggle of local SRT (quantum mechanics) and universal GRT (gravitation). Using one macroscopic constant H in addition to c and G only, the model describes a background free of coincidences or horizon problems. While the CCM's key parameter Omega_Lambda seems determined by SUM 'boundary' conditions, there is a chance of having already observed parts of a stationary universe: With no need for 'dark energy', this alternative explains straightforwardly the SNe-Ia data on universal scales. In addition to its currently assumed parts, a non-lensing homogeneous background of matter might fill the gap to critical density. A mathematical solution for a perfect black-body spectrum composed of redshifted microwave radiation emitted from 'dark' sources within the universe is derived; thus the CMB might exist as a special part of the extragalactic background light. Given the law of entropy restricted to evolutionary processes, an open concept is revealed to imply a 'chaotic' quasi-inflation background, embedding 'local-bang' cosmoses therein. - The SUM is shown to be the only arguable solution of Einstein's original equations without cosmological constant.