I just got a new roof, new siding and new gutters. There is a gap between the gutters and the fascia. I can see sky when I stand under the gutter and look straight up. When it rains, water pours through that gap and splashes on the window screens. I have called the contractor and I am waiting for a return call. Surely, this is not how it should be. Is it?

Nope. I installed gutters all over my home a few years ago and this would be totally wrong. If you paid those bozos to do this work, you got taken. I can not see any daylight under my gutters and they don't leak either no matter how hard it rains.

They need to come back and properly attach the gutters. There should be no daylight between gutters and house.

Tell them you will happily take them to court for improper installation and see what they do and say in return.

Take photos now when it's dry and you can see the daylight and then when it rains take photos of the water coming in between the gutter and fascia.

Pictures say a thousand words. You just may need them for the judge to properly see your problem.

Not only should there be no gap the roofing shingles and drip edge should stand proud of the fascia to prevent water from running down the fascia. Your gutters are hung incorrectly but your drip edge, bigger issue, is also wrong. GAF Roofing: The Importance of Drip Edge for Roofing - YouTube

Roofer or gutter installer needs to get back pronto. As the other posts have noted, no gap and about 1" of roof extending over the gutter.