Assuming the many-worlds interpretation of quantum mechanics is correct.
Using a toy problem of a Universe with only one hydrogen atom, with the electron starting near the proton.
Would the following description of the situation be accurate?
The probability density distribution of the electron around the atomic nucleus would expand at the speed of light in all directions, although most of the probability density distribution of the electron would remain very close to the proton.
Therefore, at any given moment and position in the future light cone of the proton there would be at least one Everett branch where the electron would be at that position.