The question can not be answered because it has incorrect assumptions, in my humble opinion.
First, the author is implying that, because idealism, Kant is an anti-realist, meaning that he denies objective reality, at least of space.
Then I interpret that the author assumes that, because physicists are, or should be, "idealists", any study of space as a thing on itself is absurd.
If my interpretation is correct, I would, most respectfully, find the following problems with the question:
1) To assume that Physicists are idealists.
You would be surprised on the number of scientists studying such things that have never read Plato or Descartes, let Kant alone. But, many are aware of such things, should they stop their work on such grounds ? I think not. We don't know what they will find behind those doors. I believe they will actually enrich the discussion.
2) To assume that Idealism and Realism are sets of well defined ideas that never intersect, therefore they contradict.
Not even Kant presumed to know enough to reach such conclusion. Please read Kant's "The Refutation of Idealism".
I will conclude like this:
The author believes that idealism tries to disprove objective reality. I will beg him to understand that that assumes that objective reality exists / it is definable.
Idealism is an approach to reason what we call reality.
In easy words: Open your mind fully. Do not start by assuming that you know what reality is.
Then, indeed, determining the age of the universe is not possible with our current understanding of the universe. Sadly, most scientist do not understand, or care to clarify, that the current numbers and formulas of science do not permit defining such a thing as the "start of time" or the "size" of everything.
I will conclude with the words of Michael Scriven, from his precious essay on the Age of the Universe (British Jnl. for the Philosophy of Sci.Volume V, Issue 19, http://bjps.oxfordjournals.org/content/V/19.toc )
"My Conclusion is this: No verifiable claim can be made either that
the Universe has finite age or that it has not. We might still believe
there is a difference between these claims: but the difference is one
that is not within the power of science to determine, nor will it ever