Things are very simple , if you whant to argue that the universe y past infinite you would have to argue that.
I will respond to all of this, but the list is long and I will take some at a time. 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.
1 there was something before the big bang, which is highly speculative and unparsimonious.
Your resorting to the fallacy of'arguing from ignorance,' and unethically selectively misusing science such as the bgv theorem, which coherently proposes a multiverse based on evidence.
2 that this "something" is geodesically past complete. And avoids the bgv theorem.
Again as above you are unethically playing both sides of the fence, In the above you challenge the conclusions of the bgv theorem, and here misuse it to justify your conclusions. Like others who have an agenda must realize that the bgv theorem is not gospel and completely accepted by all scientists.
The bgv theorem does NOT conclude that our
physical existence is not past infinite, and as cited it acknowledges alternative alternatives to the nature of our physical existence beyond our universe. Your not acknowledging the clear and specific reference I provided that the authors stated that the bgv theorem ONLY applies to the universe have a beginning, and NOT the multiverse, and NOT an 'absolute beginning' of anything.
3 then you have to deal with the second law of thermodynamics, if the universe is past eternal then why don't we have 100% entropy?
Your ignorance of science here is appalling, It is fundamentally known that the Laws of Thermodynamics only apply to the Macro world of a time space relationships of energy and matter of our universe, and NOT to the Quantum Mechanics of the world on the Quantum scale, which would be the nature of existence beyond any possible universe including our own..
There is a relationship between these to two scales of our physical existence, the Thermodynamic Laws do not limit.the energy matter relationships on the Quantum level.
Quantum thermodynamics is the study of the relations between two independent physical theories:
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, and I may address this more in the future.
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.