Tim does know what he is talking about. You can use a flat-bladed shovel to
score around the area. Then use the shovel to lift the grass, like making
your own sod. Fill the area until level and replace the grass. You will have
to treat the grass just a new sod until the roots re-establish themselves.

I have used this method to level small areas in my lawn. It is too labor
intensive for large areas. I would suggest repeated top dressings if you are
a patient person. If you are looking for more immediate results, then fill
in the area and then reseed.