I can only answer the above by saying the obvious:
We don't know what we don't know. That's why estimates of the age of the universe have been modified again and again over the years. Stay tuned!
At one extreme, we cannot know the age of the universe ... unless and until there is a totally satisfactory solution to
the problem of induction (there is no guarrantee that the implicit or explicit solution employed in science, or part of it, will be satisfactory to you, even only once).
At the other extreme, the estimated age of the universe IS 13.69 +/- 0.13 and 13.72 +/- 0.12 Gyr (it's a particular estimate, arrived at using a method described in the paper in which it is published).
In
my earlier post, I wrote about what the stated estimates of uncertainty mean, and how the age estimate itself is model-dependent (change the values of the parameters in the model, and the estimate will change; change the model itself, and you will have a different estimate).
Your post (which I'm quoting) seems to be about something in between; still science-based, but beyond even classes of models (and methods).
It's an interesting space!

I'd like to explore it more, but I don't think this thread is the place to do so, and in any case, I doubt I'll have enough time and opportunity to do justice to it today (i.e. stay tuned!).