So we have observed eternalism or is it just if we assume it...?
I am not sure you are aware of this or not.
The Big Bang models, of which there are currently 4 models, so far:
- from the original model of the 1920s (which would include the Friedmann Equations & the FLRW Metric, Redshift & the Cosmological Principle),
- to the 1948 model (which included the Primordial Nucleosynthesis, Cosmic Microwave Background Radiation & the Hot Big Bang),
- to the present models (the Inflationary Model of the early 1980s, and the Lambda-CMD model of the late 1990s)…
…all these models have only PREDICTED and OBSERVED the
Observable Universe.
The Observable Universe is what our technology - past & present - have managed to explain, postulate, predict and observe…so far. But astrophysicists don’t discount the probability that the universe could even be larger, and even older than current estimate. That estimate come from the data releases (in 2013 & 2015) of Planck probe (known as the Planck Surveyor, launched from 2009 to its deactivation in 2013) mapped the CMBR of the universe to be 13.798 billion years.
Planck had a much high resolution instruments than the earlier space telescopes, the WMAP (Wilkinson Microwave Anisotropy Probe, from 2001 to 2010), and the COBE (Cosmic Background Explorer, from 1989 to 1993). WMAP calculations have pointed the universe to be 13.772 billion years, in 2012 data release.
The Hubble Space Telescope (1990, still active at present) calculated the universe with estimates in 1999, between 9 & 14 billion years.
Prior to 1999, astrophysicists have estimated the age to be anywhere between 7 & 20 billion years.
All those estimates are based on observations and calculations, of the “observable universe”. Cosmic Microwave Background Radiation is the earliest phenomena that can be “observed”, and what are being observed occurred 378,000 years after the initial expansion event - the Big Bang. All that blackness that we observed in the visible light ranges, actually have most interesting information about the early universe, the universe before there were stars and galaxies.
The CMBR maps are images of the remnant heat or energy signatures of decoupled photons that have been highly redshifted towards the microwave spectrum; that heat or energy is called the Black Body Thermal Energy. When it was first predicted by Ralph Alpher back in 1948 with Robert Herman, the black body thermal energy was 5 K (kelvins), but with WMAP & Planck, this is now 2.725 K. Alpher & Herman were the ones who predicted CMBR, which was only discovered in 1964-65 by Arno Penzias & Robert Wilson.
Basically the Microwave Background was the result of the universe was cool enough to form neutral atoms, when electrons bonded with the nuclei of the light elements (mostly hydrogen, as well as helium and traces of lithium), but that also decoupled the photons, those photons are so redshifted that it can only be observed in microwave spectrum.
Those observations have pointed to the Universe. We currently don’t have technology to see beyond the observable universe, so we don’t know how much larger the universe really is, nor do we know how much older the universe is, and WE CERTAINLY DON’T KNOW IF THE UNIVERSE IS ETERNAL!
Those very theoretical models that proposed the eternal universe, are still in the hypothetical phase…there are currently no observations, hence no evidence, that the universe is eternal. We simply don’t know, which would mean these theoretical models are speculative at best.