If you're not in a huge hurry to get it done you could spread a 1/4" or a little more of top soil over the area every couple months. Just can't do too much at one time or you might smother the grass. If you want to do it all at once I would wait until closer to fall as that is the best time to reseed.

Hi,

what would happen if I put it all at once and re-seeded?

would smothering the grass cause a problem?

plans are to install an irrigation system asap.

thanks

You could rent a sod cutter to remove the surface sod, then add the soil, water it down and level it, add more soil as needed, and replace the sod on top of the new soil.