How can you verify the theories presented on TV shows like "How the Universe Works" is current and/or valid? There are many TV shows such as "How the Universe Works" that explain theories about the origin of the universe such as the Big-Bang Theory.

What resources can I access to verify the scientific thinking on the origin of the universe theories presented on such TV shows?
Use other, more scientific sources.

You have no way to test them by some home measurements - science was tuned to pass even more sophisticated tests.

Popular media is often not very exact. They try to open the results to the public. For example, to find the geometry of the Kerr Black Holes was a decade long work for the best mathematicians of the time. The result is a relative simple formula, which is understable with not far more than high school math. Most in the popular media about the wormholes and white holes is based on it, or at least strongly related to it.

So, to check it, best if you try to find the formula and try to learn, what does it mean. It still doesn't need to understand the decade long work behind that, and also this is amazing - but only after you've understood it.