If space is discrete, then there is no space in between. If you shift a bit to the right or left, it does not pass through some in between space, it disappears in one position and appears in one next to it.
Similar to Richard Feynman’s famous answer to the question “why do I feel the force of a magnet from several inches away?” What counts as a satisfying answer depends on the person, but the general answer is “that’s how the physical world works.” This one doesn’t particularly feel like a “paradox.”
With my feet, usually.
Solvitur ambulando, as St. Augustine and/or Lewis Carroll would say.