Yes I am using a word somewhat differently than you might expect.
You are using the word in two different ways, as suits whatever you are trying to claim at the time. That's called an Equivocation Fallacy, and you need to stop doing it.
And your brain explodes.
When I say time has been traversed it does not mean traversed by an entity. It just means that it has existed and something could have traversed it.
It existed. There is no justification for your claim that something could have traversed it - and you just agreed that nothing needs to do so.
When Einstein imagined riding on a beam of light good thing you weren't there to tell him it is impossible to ride on a beam of light.
True; But his entire argument didn't rest on the claim that something must have ridden on a beam of light. Your entire argument DOES appear to depend upon something having to traverse the infinite past - which we agree is impossible. Where we disagree is that you think it is necessary in order for that infinite past to exist (except when you don't think it's necessary because it exposes the illogic of your claims).
If the claim is that the time in the past was infinite that means it is possible infinite life forms existed in the past.
No, it doesn't. That is a completely unjustified and bizarre leap of illogic. Even in a finite past, our best theories suggest that life forms have existed only for the most recent fraction of the whole.
Do you also think it is possible that an infinity of organisms existed in the past?
Yes, it's possible; We have no idea what happened before the Planck time. Do you seriously think that that is necessary for the past to have existed; Or that that has ANY bearing on whether it was finite or infinite? You are just babbling now.
So if something always existed that means it is possible an infinite number of life forms existed in the past.
Yes, it's possible. It's completely irrelevant to the question of whether the past is finite or infinite though.
Do you also think it is possible an infinite number of organisms existed?
'Possible' is a low bar; so yes.
We could in theory count them all and get a grand total of "infinity"?
There exist an infinite number of integers; But we could not, in theory, count them all - and nor do we need to in order to prove that they are infinite.
Or in your religion is the only infinity that is possible infinite time?
I don't have a religion.
I'm trying to get a handle on the magic religion of "no beginning".
Then you are in the wrong place. The hypothesis that the past has no beginning is not disproven; It remains a possibility. Whether you like it or not. Reality doesn't care what you like.
How exactly would we be able to conclude something had "no beginning"?
Conclude? It's an hypothesis. It is possible until proven otherwise; We conclude that it is possible that the past is infinite, because there is no evidence to the contrary - The arguments presented so far by you in this thread don't constitute evidence because they all exhibit logically fallacious reasoning.
What evidence would make us conclude there was no beginning?
The absence of evidence that there is a beginning.
"Untermensche doesn't like the idea of an infinite past because it makes his head hurt"
I don't like the believers in "no beginning".
They are unable to reason about simple things.
They believe an infinity can be traversed.
Who are "they"? Nobody here has expressed any such belief. You are arguing with imaginary opponents.
Have you considered seeking professional help?
You are one of the lost believers.
No, I am open minded on the question, and have no firm belief either way. It is possible that time is either bounded or unbounded in the past. I incline towards the latter interpretation, but I know that either is perfectly possible.
You think it is possible that an infinity has somehow been expressed.
I don't think that at all. I think it is possible that the past is infinite; But I don't think time is the kind of thing that can be 'expressed', so if I thought that, I would be making a category error. But I don't, so I'm not.
And you believe it based on no evidence.
It is pure faith.
I do what anyone with no hard evidence should do - I remain open to all of the possibilities. You have eliminated one on the basis of poor reasoning - and you need to stop doing that unless you enjoy people laughing at your foolishly dogmatic positions.