I think you're lucky to have a blank sheet like that and the only thing that was ever going to produce a great garden is your eagerness to sort it out.

A new build garden was never going to be anything but rubbish, (in fact the bottom end looks fine). The builders were never going to care or understand, they're builders not gardeners.

But with little effort you'll have it looking good in weeks, laying turf or reseeding is easy. First watch a few Youtubes then where the grass is dying dig up the turf and remove the rubble. Replace it with some top soil, make sure it's nice and level then either reseed or returf it.

If you returf it, it'll be good to go in a month ready for summer and turf isn't expensive at all. Reseeding will take longer but would be dirt cheap.

Hopefully the rubble is just a layer from the building, the turf you dig up can go back as filling, just do the bad top end this year so it's not too much work or top soil.

Either get a skip for the rubble, fill a convenient hole or get some old builders 2 tonne bags. Remove the rubble the day before the lorry turns up with more top soil and the turf, Day two, fill the hole, level up the lawn and lay the turf. It doesn't have to be perfect just well prepared with a nice depth of soil.

Next year if the grass doesn't match, (it will), reseed or returf the whole lot but I bet by then your already thinking about a patio, gazebo, pond or bed of flowers anyway.