The BB is not relevant to the first part of the sentence which is referring to a hypothetical Steady State universe that had no beginning, but the second bolded part is referring to the universe, not a hypothetical one.
If this BB universe you live in were to not exist, Polymath is saying there would be no existence.
So if there was a BB beginning to the universe, it arose out of non-existence.
No, your question was simply generic "universe", you and
@Polymath257 never said anything about ANY SPECIFIC COSMOLOGY, with your question and his answer.
Ok, so if the universe never began, what would have existed?
You see, your question was unspecified as to the type of cosmology - no BB, no steady-state, nothing.
So, Polymath257's reply to THAT SPECIFIC QUESTION YOU HAD ASKED, did not specified any cosmology:
If the universe exists and never began, the universe would have existed for an infinite amount of time (or, potentially, time would be circular). if the universe did not exist, then there would be no existence.
Again, no BB, no steady-state, no other cosmologies were ever specified in his answer (what I had highlighted in large letters).
You wrote that "if the universe NEVER BEGAN", his answer was "THEN THERE WOULD BE NO EXISTENCE".
What do you think "never began" mean, Ben?
If the universe "never began", then the answer would be simple, there would mean there were "no universe".
And you complained that English is my language. You don't even understand the words you used yourself.
The "never began" would be no universe - our Universe, now, would exist, because there are no eternal universe, no Steady-state cosmology, no Big Bang cosmology, no Multiverse, nothing.
It is funny (as in ironic) how you accuse anyone who disagree with you, don't understand English, when you don't even understand what you are saying.
LOL
Not only did
@Subduction Zone corrected you where you misunderstood Polymath257's reply, he had to clarify what you keep misunderstanding:
Let's be clear.
The universe *is* existence. Anything that exists exist *within* the universe.
So, if the universe (BB or not) did not exist, there would be no existence. That does NOT mean there would be a 'state of non-existence'. No such 'state' would exist. But, in fact, things do exist. So existence actually does exist.
Again, this has *nothing* to do with BB cosmology.
'Non-existence' simply does not exist. Anything that exists has existence'.
And, to clarify further, if the universe had a beginning (like it does in BB cosmology), all that exists is after that beginning. There is no 'state of non-existence' before simply because there is no 'before' at all.
You seem to be desperately trying to show that BB cosmology implies there *existed* a state of non-existence before the BB. And that is simply not the case. No such state existed because *there was no before*.
I don't think you are only misunderstanding, I don't think you are being intellectually honest with us, because you had deliberately twisted Polymath257's words, repeatedly when you were replying to Subduction Zone and me.