The first two paradoxes above can all be accounted for, fairly neatly, by the basic properties of fundamental physics, especially quantum physics. The third is not quite so easy.

The first paradox: There can be no effect without a cause. Whatever events transpired near the outset of time, each must have been caused by some prior event. So we can never attain an account of the very beginning.
Causality is not a requirement of the fundamental laws of physics. In the macroscopic world, causality works, due to the massive number of elementary particles involved in any interaction, which cancels out any odd funny stuff at the individual particle level. But something can happen that didn't have any cause, it's only a matter of probabilities. The Copenhagen Interpretation is the more-or-less canonical view of quantum mechanics currently, and it addresses this somewhat.

The second paradox: You can't get something from - or for - nothing. The "origin" of the universe, if that concept is to have any meaning, must create the universe out of nothing. Therefore there can be no logical explanation of genesis.
Yes, you can generate something from nothing. Zero-point energy exists, and it comes purely from an empty vacuum of space, due to, again, quantum indeterminancy encoded in the Heisenberg Uncertainty Principle. There might not be a lot of energy there, but you can in fact get something out of nothing. Just getting a lot of something out of nothing is unlikely.

The third paradox: Regardless of its net energy, the universe must have originated from another system, and that system must in turn have had an origin of some sort. And so we are caught in infinite regress.
This one one can't say much about. Even if the universe began as a massive vacuum fluctuation in some sort of primordial vacuum, one can always ask what set up the laws of physics the way they are. That's really where we go past what modern science can say. Eventually, no matter what path one follows, one has to declare 'that's just the way it is', whether on a religious or a scientific basis.