Yeah, yeah, sudoku is easy for computers. That's not the point. The point is learning about neural networks. So yeah, "adding a neural net" does help with that.
In which case the hard part is finding a suitable problem; you might be better off learning about SMT solvers because you don't have Marc Cuban telling everybody to do it.
Pick one open square, try a number that is possible for that, backtrack if you get stuck.
For better results, pick the open square which has the fewest number of possible choices.
Human solvers might try something more efficient, but the above strategy is not at all bad for computer implementation.
It's very much a solved problem with existing technology, see
https://en.wikipedia.org/wiki/Satisfiability_modulo_theories
adding a neural net to it doesn't help in any way.