The video on the left is typical of some of the misinformation around about the Big Bang theory and the Catholic understanding of it. Here are some of the errors and why they are errors.

There was no singularity: According to wikipedia there are two candidate theories for this:

Loop Quantum Gravity: "There is no experimental observation for which loop quantum gravity makes a prediction not made by the Standard Model or general relativity (a problem that plagues all current theories of quantum gravity)." In other words, there is no particular evidence for it, and it doesn't work, "Because of the above-mentioned lack of a semiclassical limit, LQG has not yet even reproduced the predictions made by general relativity." 

M-Theory: "Attempts to connect M-theory to experiment typically focus on compactifying its extra dimensions to construct candidate models of our four-dimensional world, although so far none has been verified to give rise to physics as observed at, for instance, the Large Hadron Collider." In other words, there is no evidence for it.

Even Stephen Hawking talks about singularities on his own website.

Which leaves this video based on speculation and not evidence.

He makes it clear that our understanding breaks down before the expansion of the universe, but goes on to hypothesise that "experimental evidence does not rule out the possibility that there may indeed be a time before the beginning." This is where there are many inconsistencies. "A time before the beginning" makes no sense, but lets say there was time before when we currently think time begins and during this time there is some kind of massive contraction before the expansion. Again, no evidence and it flys in the face of the evidence we have which points backwards in time without being able to make any sense of when time equals zero. His point is that we don't know what happens at (or just after) time equals zero. We all agree on this. So he suggests it is better to accept theories without evidence that don't explain all the evidence than to just say we don't know.

The alternative is believe in God. But this is not a scientific alternative, but a philosophical one. We have explored this sufficiently in this article. But to just summarise the discussion for now. Science can never prove God since that is beyond the scientific method. Lemaitre very clearly believed this and so was able to convince pope Pius XII to not make pronouncements on scientific cosmology. But it is possible philosophically to use this evidence to come to belief in God. It is wrong to believe in God of the gaps, ie to believe that God fills in the gaps of science. Catholic understanding can accept an eternal universe (St. Thomas Aquinas saw no incompatibility of it with Catholic theology if it was the case). So the video is incorrect about Lemaitre needing to revise his theories since he lets science do science and religion do religion. Lemaitre modified his theories on new evidence and so would have no problem with revising this theories (if he was still alive). 

The view that religion is tries "to explain the things science can't" implies that religion is about a God of the gaps which Catholicism isn't. It is partly true that religion does explain things science can't such as why God created the universe and to assert that God did create the universe which science can't disprove nor prove using science alone. Just as  "experimental evidence does not rule out the possibility that there may indeed be a time before the beginning" so too it does not rule out philosophically there is a God.

He goes on to suggest that physics might be "nudging us to the view that the universe is eternal." There are some currently inadequate theories that point in this direction, but as has been shown, there is no issue of belief in God and an eternal universe (see Aquinas and the Big Bang). There is still the unavoidable question, "Why is there an eternal universe?" To avoid the question is to answer the question in a way that is based on various attitudes and presuppositions. But God is a very good answer to this philosophical question.