Ok unless you clarify otherwise, I will take your answer as an admision that cyclic models are probably not "past infinite"
Now is my turn please provide an example of something that I haven't answered
Not necessarily past infinite.
Considering all the physicists and cosmologists,including the ones you cited believe the evidence demonstrates that our universe and all possible universes form from previous existing energy where is the scientific evidence for any beginning without a cause?
You have not responded to the following:
In summary the reflect Christian Creationist apologist agenda, and not legitimate science and math. All known causes for the beginnings in the nature of our physical existence have an adequate natural explanation. No unnatural explanations have been discovered.
It is fundamentally unknown whether the nature of our physical is infinite and eternal or not.
thermodynamics and
quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905
Einstein argued that the requirement of consistency between
thermodynamics and
electromagnetism[1] leads to the conclusion that light is quantized obtaining the relation {\displaystyle E=h\nu }
. This paper is the dawn of
quantum theory. In a few decades
quantum theory became established with an independent set of rules.
[2] Currently quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. It differs from
quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium. In addition there is a quest for the theory to be relevant for a single individual quantum system.
The Laws of Thermodynamics are described as emergent from the Quantum World.
A more technical article on this describes the relationship here;
https://www.sciencedirect.com/science/article/pii/S2211379718312117
It also addresses the question of the Boltzmann constant you erroniously assert below.
4 if the universe is eternal, then it would be dominated by Boltzmann brains, implying that you are almost certainly a Boltzmann brain, and that the world that you inverse is an illusion.
Answered in the references above,.
5 if there was "something eternal " before the big bang then it remains inexplicable why did the big bang occured 13B years ago. How do you go from - infinity to 13b years ago?
Very very confusing, but cutting the Gordian knot.the nature of our universe does not determine whether our 'physical existence' is eternal and/or infinite.
6 you would have to show that the concept of an actual infinite is logically coherent.
Actual infinities are not logically incoherent, but the attempt to miss use actual infinities to limit the nature of our universe as not past infinite is incoherent and just plain bad math. Actual infinities are closed sets of infinities, which cannot limit potential infinities. Our physical existence is potentially infinite. This is fairly simple high school math first defined by Aristotle.
While if you grant that the universe is past finite you can avoid all of these points , things are simpler if you accept that the universe had a beginning
Based on very real science and math, simply NO. The question of whether our 'physical existence' is infinite and/or eternal is unknown,and definitely cannot be answered by assertions of outdated Christian apologetics.