You wrote, “hence time cannot have a beginning”
This is merely your opinion and I disagree with it since I believe that time had a beginning, just as I believe that “space” had a beginning.
Time may or may not have an ending, I do not know.
If you want me to “prove” that time has a beginning, no problem, I can’t do it?
By the way, what is “objective time”?
Would you consider back in the past when you first wrote this post of yours to be objective time, subjective time, neither or no time at all?
Would that past, when you first made your posting, be a part of the time that you claim does not exist or would it be part of no-time that does or doesn’t exist?
Ever thought that all of these things that you think up of as not existing may very well exist and it is you that do not exist?
I happen to believe that you exist, by the way, are you a politician or a philosopher or both or neither?