As others point out, Zeno's paradox shows that given certain common-sense implicit assumptions, movement seems impossible. Quite obviously too, movement is possible; therefore one or more of the assumptions must be false.

Others have pointed out that it may be possible to pass through an infinite number of in-between locations in a finite duration of time. We can calculate the maths of that with integration and limits, but even if we couldn't, that wouldn't rule it out: not being able to prove that it is possible is quite different from proving that it is impossible.

There has been discussion on the possibility that there are not an infinite number of in-between locations. But this is **known** to be the case. Distance is discrete at very small scales. So is time.

The minimum distance that one can move in any meaningful sense is called the Planck length. It is around 1.6 × 10^{−35} metres.
This has been known for around a century - Max Planck was awarded the Nobel Prize in Physics in 1918 "In recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta." So this topic of Zeno's Paradox really is quite dead.

This says nothing about how big the universe is, or if it is infinite or not; or which kind of infinity it might be, just that it does not have infinitely small subdivisions. If the universe is a simulation, that's how big the pixels are.

If you're not into the metric measurements for the Planck length, then 6/10000000000000000000000000000000000 of an inch is about right; if you need scientific accuracy then use the metric measurement already; that's what it's for. Put it this way: the Planck length is about 10^{-20} of the diameter of a proton, which itself is about 1.65* 10^{−15} m. Shrink down to the size of a sub-atomic particle and you're not even halfway finished shrinking yet. The Planck length can be precisely described (as "1.6 × 10^{-35} metres") but it really doesn't fit into the human imagination.