While the second week of September is supposed to be the best time for fall seeding (according to our neighbor, a sod farm) we have planted as late as the last week of September and had it grow. I'd wait and see if it is a long warm autumn. If so, I'd toss down some conservation mix on the bare soil along with a light straw or hay. If not, or the house is later than expected (don't be surprised if it is) I'd get a bunch of hay bales (look for inexpensive mulch bales) and spread thickly. The goal is to prevent erosion during snow melt and spring rains. Then plant in spring, though since the ground is cold in early spring, you'll have to wait a while, and then water during the summer. You will find that much of what you have there now growing will be buried under piles of dirt or construction materials, so may not look too good, but roots may survive and there will certainly be a good seed bank as well. If you have trees near the site, put up fencing around them as far out as the dripline to prevent root compaction from the soil being driven over or parked on.

Listener,
I am assuming that right now you still have a big pile of top soil sitting somewhere in your yard (or if lack of space is trucked away until a later return date) and that your drive way and walks have yet to be determined. Have your well, electrical, phone, and cable, lines been laid and brought into your house? Has your septic line been connected to the housed? Once this outside trenching work has been completed you should have your contractor schedule to spread your top soil ideally in the 1st or 2nd week of September, or if it isn't part of your contract plan on spending a couple of long days doing this yourselves.

After you spread your top soil you will want to rake through it a couple of times to remove rocks, roots, ect with a special rake designed specifically for this task (sorry I forget the name of it). Spread your grass seed (a local mix is your best bet)then rent one of those rolling drums that you fill with water and roll over your entire lawn. Now is when you will want to invest in multiple hoses as moving your hose around without wiping out large areas of newly planted seed is
IMPOSSIBLE. Keeping your seed consistently watered is the key to getting your grass to grow before the weeds move in so if you can you may want to get some on/off timers for your hose.

After all of your hard work you may want to remind the contractors who will still have a month of finish work ahead of them to no longer park on what is now the front lawn. I would also mention that if you were planning on laying gravel, asphalt, ect for your driveway on a later date sometime after you have moved in, plan on a massive amount of loose dirt from the driveway being brought into the house by workers as well as yourselves. The contractor will lay down paper after your floors are done and some will even make sure every worker remove their boots but you will soon see this is a big issue and will want to finish your drive asap so if you can budget for that now.
Congratualations on your new home!!

I'd say to hire a good landscape designer and have a plan drawn up for the property. Then prioritize what you can accomplish this fall based on how the weather progresses. Some things have to happen in their own best time and conditions. Don't just start plopping things into the ground. The big picture is important.