Had s similiar issue. Fathers house had a sewer line ran giant trench. His yard is zoysia so we put some sifted soil and lightly graded and compacted it by hand. Applied some fertilizer and sod and kept it wet daily. Took root just fine. Make sure your sod matches the season. Fescue now zoysia/Bermuda in the spring or summer time.

If the grass is covered with soil, it should be smothered and will die. Once that happens it should be okay to sod over top. You can check by digging down through the soil to see what it looks like.

When the refilled the trench they should have put all the soil back in that came out. What the uninformed trench diggers do is fill it to level and spread out the "left over" soil over the area outside of the trench. It should all go back into the same hole or it will settle exactly like yours did. I've had it done both ways - mounding works. It can take 3 years to completely settle, but it will.

I'm not sure what darktower is saying about sod matching the season. It should match your existing grass regardless of when it's put down.