In CP-SAT the equivalent to min() is:
add_min_equality (self, LinearExprT target, Iterable[LinearExprT] exprs)

Bonus tip:
CP-SAT also offers constraints such as
add_all_different ()
which will simplify your model significantly.

IIRC, there is actually a soduko solver in the samples section (on ortools’ GitHub).

Good luck and happy holidays!