So I would just like to make a few points regarding some things you've said.
If it is both simultaneously true that radioactive isotopes decay without a cause, and we cannot apply the law of physics to the early universe, then there is no reason to apply the facts about radioactive isotopes as being relevant to this discussion in regards to causality and the early universe. Whatever models we have of physics or causality, or lack thereof will not be relevant based on this reasoning, because they, according to you, break down. This sword cuts both ways...
Secondly, you say that it has not been demonstrated that everything that exists has been actualized by a prior cause... Unless you can empirically provide an example of being coming from non being, or something being actualized from nothing, this is really just an argument from ignorance. What you're in essence arguing in this:
We have not seen every single example of a triangle, therefore the claim triangles have three sides is unproven.
Well that would be fallacious. We don't need to experience every single triangle before we can state they have three sides. It's definitionally true. Whether we accept the axiom or not.
As I argued earlier, the causal principle is confirmed by inference, but it's definitionally true based upon what we are dealing with. Non being cannot bring about being... It's non being.
In regards to premise two, did the universe have a beginning, you seem to have cast doubt on the BGV theorem...I am not a cosmologist so I will grant you this. What we still have though is the second law of thermodynamics.
In short, the universe is rapidly approaching a state of complete entropy. If the universe were eternal, we would have been in that entropy by now. Another way of looking at it, the usable energy in the universe is running out. If the universe were eternal, we would have run out by now.
Now, moving on to the possibility of an actual infinite:
There are several different ways this can be fleshed out, but to be succinct, there are two types of infinity. A potential infinity and an actual infinity. An actual infinity is never instantiated. There are several reasons:
1. It would lead to absurd and impossible consequences.
Suppose I had a library with an actually infinite number of red and blue books. Now suppose I subtracted all the blue book (an infinite amount) from all the red books (an infinite amount). How many books are left? An infinite amount still.
So in this instance infinity - infinity = infinity.
But now let's say, I subtracted every book greater than 3
How many books do I left? 3.
So in this instance infinity - infinity = 3.
This leads to a logical contradiction
And because logical contradictions cannot be instantiated in reality, it follows an actually infinite series of things, cannot be instantiated. But it gets worse. Suppose for a minute we imagine the universe as past eternal. That would mean that everyday prior to today went on into infinity. If we look at the reverse of this, in order to get to today, there would be an infinite number of past events to traverse.
And that simply isn't possible. There would always be one more event to cross and complete before we could arrive at the present. Which means we would never arrive at the present. But we are in the present. So the number of past events leading up to today was finite. We couldn't traverse an infinite.
I know this post was lengty. but I tried my best to explain why I think premise one and two stand. Thoughts?