The universe is temporally finite, but spatially infinite.
Yes it is hard to understand, basically it means inflation has caused expansion faster than light so the boundary
(if there even is one) will forever be beyond our detection.
This is a inescapably a paradox of reasoning in itself.
It is however the scenario that fits the evidence.
It's a conflict also that there are two problems that exist in our understanding of the universe.
The first one is there is a conflict in the age of the universe.
Some stars appear to be older than the universe itself temporally by some calculations.
So there is a error in one. Paradox.
The other is the speed of the stars at edges of galaxies, they move to fast, we attempt to explain it with dark matter, it may be the answer, but is not beyond scant evidence in proving it to be the cause. Or even exactly what it is causing it.
The uncertainty principle, and Schroeder's cat the Higgs field, all enigmas and also paradoxical. There are many, and whether you accept it or not , the start of this universe is a paradox.
We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe.
Not a paradox, Einsteins formulas predict it, objects change in position relative to the space-time grid. The speed of light is a constraint for objects that exist within space-time, not for space-time itself.
So not paradoxical
The other is related and can be calculated by the Hubble constant at around 71MPS. The expansion of the universe predicts that objects over 4200MPS away will be moving faster than the speed of light.
Again not paradoxical
As I have shown you by offering the definition that a paradox is self contradictory statement. And therefore I will repeat, just because the beginning of the universe is not understood does not make it self contradictory, it just means its not understood (yet).
As to the uncertainty principal, Schroeder's cat, one theoretical, the other an example to explain the uncertainty principal on the quantum level. And why is the higgs field a paradox? Elusive, true, paradoxical, nope it has been predicted for years