How did Omega get a body?

I don’t want to be one of those who just hate the newly gone Doctor for
turning a grim Sci-Fi series into a fairytale musical without even better
reasons, so I try to find those better reasons at least.

Here’s one potential reason: Last time we saw Omega, he was trapped in the
very opposite of a universe, with no body and no chance to return. One
would think the Rani and especially several Doctors knew that. However,
“The Reality War” basically revolved around the idea that the Rani just
digs into time and space deep enough to extract his DNA. To absolutely
nobody’s surprise, he suddenly was able to return to Earth with a body. Is
there any canonical explanation on how that could happen?

(I’ll leave the other plot hole, Omega “feasting” on time lords, for later.
I mean, that would be a really short-lived feast as far as we know.)