The hypothesis of Big Bang is not the only possible way to visualize the Universe at the largest possible scale. If the James Webb telescope will fail to discover "end of light" and confirm it the revolution in the astrophysics is inevitable. The red shift may be easily attributed to non-zero mass of photon (old abandoned idea of tired light, but on new physical principles, not yet discovered), microwave background may be something completely irrelevant but what about the generation of the energy in stars?
Indeed, if the stars are only generating energy and the Universe is much much older than expected (say trillions of years or even older) how it is possible that stars are still shining? They would be completely depleted long ago.
So it is necessary to hypothesize the reverse process - how energy is converted back to matter (it is assumed for now that the energy conservation law rules supreme and E=mc*c is valid with very high accuracy).
Actually the only plausible hypothesis except for completely new processes to be discovered is connected with well known phenomenon predicted by Soviet academician V. I. Goldanski and confirmed later in USA- the two-proton decay. Indeed in this process the nucleus may be excited by some kind of energy consuming process (say proton of ultra-high energy accelerated in the space by magnetic fields and photons from the stars) will strike the appropriate dust particle, excite the appropriate nucleus and generate two protons in the decay, thus successfully transforming energy back into the matter (and very important, hydrogen gas, which would later condense into the star and the process to be repeated again and again, pretty much like water circle on earth.
proton + energy + nucleus= nucleus + 2 protons
Indeed, the two proton decays are quite common and in the recent years they are discussed as important for the detection of neutrino [1].
In that and many many other articles the processes like multinucleon knockout are discussed, like (p,2p) and (p,3p), where the proton with huge energy generates two or three protons (and the remaining nucleus will undergo the process of more usual decay afterwards) successfully transforming the energy into the matter or even process of neutrino of extrahigh energy detection in which it is exciting the nucleon (energy absorbed) and it decays into the two or three protons plus nucleon with lower energy [2].
Essentially the processes like those may be responsible for the conversion of energy back to matter, than matter back to energy (through very easily observable stars burning in the sky) and again and again for possibly infinite time span. The important part will be notably played by the two-proton decay because this is the easiest from energy point of view way of conversion energy into the matter. No problems here from the antimatter point of view - it is not born here, the initial non-equilibrium distribution is merely preserved. Why matter predominate - it is a very good question in this picture of Universe, but as unsolvable as it is with Big Bang hypothesis - it is merely not enough knowledge now to answer it. Some amount of antimatter is of course generated during the conversion of energy back to matter, but it quickly converts back at annihilation (that would be the second, much smaller in scale and much less important cycle of matter-energy conversion). In this picture the Universe is back to the very very old ages, trillions or even more years old, possibly infinitely old. The observed non-uniformity of red shift in time is to be explained by some other phenomena (yet to be discovered) and the origin of Universe becomes the philosophical question again, rather than physical one.
The problem with this energy-matter cycle is that one part of the cycle is very visible (stars) while the second one is mainly hidden in the impossible interstar distances (slow aceleration of elementary particles with energy till they strike the appropriate nucleus), that is why our civilization successfully identified only one part of the cycle and failed so far apprehend the second, much slower part of it. Indeed, it means that at equilibrium the vast majority of energy is accumulated in wave-like particles like light (despite my another hypothesis actually demands that any matter is both matter and wave, merely barionic matter is mainly matter and only a little wave, while light is almost completely wave and just a little matter), which is actually quite accepted today (energy predominates the matter very strongly). The largest difference is the origin of such shift toward the energy and dynamic - in Big Bang hypothesis matter will eventually disappear completely while in my idea it is the equilibrium distribution.
References.
1.A.Frotscher et all "Sequential Nature of ðp;3pÞ Two-Proton Knockout from Neutron-Rich Nuclei" // Phys. Rev. Letters, Vol 125, 012501 (2020)
Sequential Nature of (p,3p) Two-Proton Knockout from Neutron-Rich Nuclei (aps.org)
2.J.E.Sobczyk et all "Exclusive final state hadron observables from neutrino-nucleus multi-nucleon knockout" // 2002.08302.pdf (arxiv.org)
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