Originally Posted by Bob F

Using weed barrier as you suggest would just limit the depth that grass can grow
its roots, making it less drought tolerant.

If you want to start it now, you will have to be serious about watering. When
you first plant the seed, you want to water very lightly until the grass is well
sprouted. This means running a sprinkler for maybe 5 minutes morning, noon, and
mid afternoon. You don't want to soak it, but you don't want the seed to dry out
and die. When the grass is well sprouted, reduce the frequency gradually. while
increasing the amount of water to get the soil wet deeply. It would be easier in
the fall, but similar "rules" apply.

For leveling whatever topsoil you add, or even the soil there already if you
don't, Rent a WIDE landscapers rake, and work hard to get it level. Using a lawn
roller to firm it up, then raking, repeat a few times, so you don't end up with
more settling producing low spots. Spots that were tilled deeper than others
will settle more unless you do something to prevent it.