"the 'first/last' of the [day/night/week, etc.]" for "the 'beginning/end' of the [day/night/week, etc.]

Question

Where in the U.S. and Canada do they say, at the first/last of [the day/night/week, etc.] for at the beginning/end of [the day/night/week, etc.]?

Luck had it that they only experienced a very minor sprinkle at the first of the day...

ccohva.org

"Breakfast” is defined in the dictionary as “a meal eaten at the first of the day.” This definition does not say when exactly the first of the day is, but the first of most students' Sundays begins anywhere from 11 am to 4 pm.

Spoon University

Clay, who had already decided she was right, looked out the barn door at the last of the day.

Cell: A Novel by Stephen King

At the first of the week, give the class 10 points to start. Keep track of points on the chalkboard for all to see. Erase a point anytime a student interrupts another person. At the end of the week, if any points are remaining, then the class gets to have the reward from the secret sack (written on the piece of paper.)

oregonstate.edu

"I wasn't figuring on these cold temperatures, though. It was so mild in the fall and at the first of winter."

Cape Breton Post

We are going to build our springhouse today and dig up some of the vegetables that we buried at the first of winter.

watershed.org

The 43rd president of the United States had paid lip service to closing the Mexican border to the illegal immigrants back at the first of the century, but nothing significant had been done to stem the tide.

Temples of Hope and Desire

We also should note that John was told expressly at the first of the book (Rev. 1:1) and also at the end of the book...

An Overview of the Book of Revelation

A man who routinely claimed he was hearing command hallucinations to inject rubbing alcohol into his veins requested admission at the end of every month, when his assistance checks had run out. At the first of the next month, like clockwork, he would sign himself out of the hospital, stating that his voices had miraculously abated.

Falling Into the Fire: A Psychiatrist's Encounters with the Mind in Crisis by Christine Montross

This is going to be the embarrassing part that I apologized to my family about at the first of the book, so Mom, if you're reading, you might want to skip this part, because the drag racing back in high school and the other things you didn't know about your daughter makes really good reading to total strangers.

I've Got My Big Girl Panties On: One Foot at a Time

“Oh you guys are lucky you stopped by. At the first of the year this was all going to be tossed out or given to another station.”

Kurt Russell and Directors Chapman Way & Maclain Way Talk THE BATTERED BASTARDS OF BASEBALL, the Feature Adaptation, and More at Sundance 2014

first n.

the beginning: We're going to The Fort for family vacation the first of June; She was a good worker from the first.

last n.

the end or conclusion: We're going on vacation the last of September.

Random House

Answer 1

I think the sources you cite are mostly outliers and not the norm in North America. Novelists often experiment with form and language and are trying to find new ways to say things, which is what I think Stephen King did here. I do believe at the first of winter is sometimes used, because the phrase as a whole has some poetic beauty to it (compression of language, and a contrast between the precision of the word "first" and the vagueness of the changing of a season). All the other quotes seem unusual to me, including the Random House example. The Bible analysis seems like it's intentionally trying to sound archaic and flowery, perhaps to match its subject matter.

It's worth noting that there is a difference between at the first of day and at the first of the day. They're both uncommon, I think. The former implies a general notion of what a day is, and as such is more poetic -- similar to at the break of dawn or since the beginning of time or at the first of winter. The latter seems to refer to a particular point in time and appears to be used mostly in Western states.

It's also worth noting that the first of the month is common, but I've never heard at the first of the month. I believe Americans would say on the first of the month instead.

Answer 2

https://www.english-corpora.org/coca/ offers 12 examples of "the first of the day" and each one uses "first" as a referent to a previous noun.

"He smoked a cigarette, the first of the day."

There are no matches for "at the first of the day"

https://www.english-corpora.org/now/ gives tons of examples of "at the first of" and some refer to times. There are several from the midwest (Arkansas, Denver), but there's also one by an author born and raised in Tennessee and currently residing in Wisconsin: Alex Bledsoe.

" a relief to be away from London, after the zeppelin air raids at the first of the month. Here in Wales, no trace of the ghastly war could"

Who's to say whether he picked it up in the south or midwest.

On the whole, though, it appears to be a midwestern phenomenon.