This article is awkwardly over-confident in its analysis and conclusions. There are now substantial and serious doubts and debates about every aspect raised, including the very existence of the Big Bang (many cosmologists now prefer different models), so, no, we don't have great confidence about the age of the universe. The one thing we can be most confident about, given the history of science, is that all of our current theories will be over-thrown by new theories -- and some that won't "include and transcend" existing theories, which is the standard narrative in the history of science from those who prefer to gloss over the history of mistaken theories in cosmology.