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?
While I can find no fault with the deductive validity of this argument - the conclusion certainly seems to follow from the premises - I'm afraid this is as successful as the argument gets. Not just one, but both of the premises commit logical fallacies which they hide in the vagueness of their formulation.
To anyone who is confused about what it is exactly that theoretical physicists do, here is a brief yet broad summary of what we're trying to achieve.
It is not difficult to find online forums and blog posts that proclaim facts and arguments as if they were certain. People of all philosophical alignments will do this. Theists will proclaim what they believe to be indisputable facts like: "Something must have caused the Big Bang", and atheists are often guilty of prophetically declaring their favourite origin story for the universe: "Quantum fluctuations produced the universe" or "Many-worlds explains fine-tuning".
There is a split in the philosophical community with regards to this issue. By and large, the majority of philosophers of physics claim that space and time are real and important entities, but there is a small faction who maintain that space and time are just useful theoretical constructs that don't have the independent existence we sometimes attribute to them.
We can get most of the way to deriving the constancy of the speed of light just from the Principle of Relativity alone. In other words, the speed of light being constant is just a consequence of the laws of physics being the same in all inertial frames.
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.