For more info, no dogs or pets are using this lawn.

How many square feet of lawn and how long does it take to hand water it?

About 500 square feet of yard and about 45 minutes to an hour or so, using a hose attachment in shower mode at max setting.

Considering that it is new sod in its first year, the pattern of the browning, and your location/temperatures, my first inclination is that you are applying too little water. It takes 625 gallons of water to cover 1000 sq. ft. with 1" of water which is the general recommended amount. So you need to be applying about 312 gallons for your yard. Just to get an idea how long you should be watering, use your nozzle and see how long it takes you to fill a 5 gallon bucket. Multiply that time by 62 and that is how long you should be watering for 1".
Regardless, you need to Immediately determine what , if anything, is attacking the lawn before applying a cure. Look at the blades of "green" grass that is adjacent to a "dead" area for lesions, powdery substances or coatings. Also look for any insects in the crowns or soil. Compare anything you find to images of diseases and insect infestation that can be located on university turf sites or from a Google search "images of lawn diseases".

If I water it at that rate, can it come back or is it too late for the heavily browned sections?

Looks like not enough water to me. You will have to either resod or over seed the dead spots.

"If I water it at that rate, can it come back or is it too late for the heavily browned sections?"

If your issue is due to drought and the crowns have not died, it can recover.

Do NOT ignore the possibility of disease. If it is a disease you must act quickly.

Will look for disease or infestation, and will water it more thoroughly. Thanks!

Couldn't find any evidence of infestation (at least none that were evident), but I did take another picture:

{{gwi:100413}}

The dirt is very dark brown/almost black.

I didn't make myself clear. You need to be looking at the GREEN grass next to the dormant/dead areas for signs of insects or disease.

Thanks for the clarification, I will have a look at it in the morning.