“There is no evidence that a single atom can be compressed into a singularity, much less the entire universe.”
Yes, but if this is the case, that an atom cannot be compressed, then there must be something unknown that prevents it. After all, in a black hole, we have already overcome all known physical forces that could constrain gravity from compressing matter further. Otherwise, it would be a neutron star, not a black hole.
So, are we missing a force that could prevent a singularity? Or missing some fundamental knowledge about matter, or space? Or can a singularity exist in the black hole, even if we can’t observe it? Only the last option seems to allow you to say that relativity doesn’t have a pretty significant omission. And if there is such an omission, then speculating about the Big Bang seems rather silly until we address the problem of black holes.
The point I’m trying to make is that a singularity is a mathematical concept, not a physical reality. There are many mathematical concepts that simply cannot exist in the physical world. There are functions that go from - infinity to + infinity in zero time. There are functions that have finite volume, but infinite surface area - you can fill them with paint, but you can’t paint them with the paint they contain. And there are singularities. In many instances, over the immense space of the universe, black holes can be treated as singularities. The mathematics of singularities will adequately describe their behavior. That doesn’t make them singularities.
The Big Bang theory treats the universe as a singularity at its start. The problem there is that the math still doesn’t work out. That’s why cosmic ‘inflation’ was invented. The math around the start of the Big Bang works out just fine, as long as the laws of physics are ignored during the first few hundred thousand years, or so. That’s not a ‘theory’, that’s a cop-out.
My preferred viewpoint towards evolution (devolution) and long ages is: