Hen Not Sitting
I have a nearing 1 year old chocolate hen and chocolate tom of the same age. They live in a somewhat small pen for most of the day. I provided my hen with a half of a large dog crate (the one that you take them to the vet and stuff with) as a nesting box. I put shaving in it. Her first egg was white and had some little calcified bumps, and was outside the crate. The next was inside the crate, not in a nest, and it looked more normal in shape, and it was white with pink dots. The egg she laid today (the other was yesterday and the first was last Thursday) was way far from the crate but looked like the second one. I keep shaping a nest for her in the shavings and putting the eggs in but she doesn't seems to care about the eggs. Is this normal for a hen's first eggs? For her not to be broody after almost a week since her first egg?
This is very normal for a hen that is laying for the first time. Eggs may be dropped wherever she happens to be when the egg needs to come out. It can sometimes take quite awhile before a young hen figures out what is going on.
It would be very unlikely for a first time hen or even an older hen to be broody only one week after laying her first egg. Each hen has her own built in clutch size requirements. Many will go broody once they have made a clutch of 8 to 12 eggs. Others can broody on just a couple of eggs or if they have been laying long enough even a single fake egg will do. Then there are the ones that need a clutch that has 15 or more eggs. One of mine did not go broody until she had more than 2 dozen eggs in her clutch.
With your hen having not yet realized what is happening to her, I would not expect her to go broody until after she actually makes a nest. She may or may not decide to use the nest that you have made for her.