If saving the grass is not an issue, then do it right over the top. Any mineral based soil will work. Topsoil or sand, or a mix, will work. Leave out compost and mulch. They are fillers that will provide no volume in a year. If you use something significantly different from your present soil, you will see the difference from now on. My soil is awful - so awful that the sand I used to level it shows up as a green spot on one side of the lawn. Yellow on the native soil and green in the sand.

To allow for settling, you will need to mound the soil up a little in the middle. How much is hard to guess, but if you make it perfectly level now, it will be a hole again in 3 years. Try filling, watering to settle, refilling, and rewatering. It will still settle for the next 3 years.