Since you're going to be putting down topsoil, I would kill all the
existing growth with Roundup. A week later, you can mow it short,
then put down the topsoil and reseed. Don't know where you are
located, but it's getting late to start this now here in the
northeast. It will need a lot of frequent watering as the temps get
warmer and there will be more competition from weeds.

Early fall is by far the best time to do this type of project.