The Astronomer Hubble for whom the telescope was named after, discovered that the Universe is actually expanding. This expansion was proved using a process known as the red shift The doppler effect of galaxies receding from us and each other simultaneously was found by the shift at the red end of lights wavelength.
If therefore the Universe is expanding and is likely to be accelerating as it expands. What is it expanding into. The paradox suggests that effect observed by Hubble is that it is the empty space that is expanding, not the matter within that space.
We can only conclude that the Universe must have an edge but what is beyond the edge. I have given this much consideration and can suggest a way of looking at this problem.
There are infinities within infinities as numbers are an example. These infinities are classed as sub infinities . Within the sub infinity there are limits encased in the larger infinity. For example there are an infinite number of fractions between one and two but one and two are the limits.
Maybe the Universe is the similar. There is an infinite expansion within limits. Hopefully one day we will find out for sure.