Here is one of my recent articles in a nice, condensed visual form. While baryon asymmetry is an intriguing unsolved problem in modern cosmology, it does not endanger the Big Bang theory in any significant way.
So how do we explain the fact that there is more matter than antimatter in the universe? The fact is that currently, we don't know. This is called the "baryon asymmetry problem" of cosmology.
While it's always healthy to be sceptical about things and to re-examine the evidence supporting your science, it seems a worrying number of people are taking this far too far. The bottom line is that there is a wealth of evidence that supports the Big Bang theory which no other known theory can explain.
This is why I say that the universe must contain time. The universe is best thought of as a static 4-dimensional shape of which slices are all we can perceive. What really bites is that we all perceive different slices of this 4-dimensional shape, and how would that be possible if the universe were only 3D?
I've seen it come up several times recently. For some reason it seems that many people think that the second law of thermodynamics is a major problem for our existence.
Although the purpose of the Drake Equation is to estimate the number of alien civilisations with which we could potentially make contact, in truth we have absolutely no idea how many alien civilisations are out there.
It is almost certainly the case that time behaved differently at the Big Bang singularity to how it does now, and that it is not possible to define a time "before the Big Bang". Defining a time before the universe would be nonsensical anyway because time is a part of the universe, not external to it.