With questions like this, I like to turn to the Ngram Viewer
https://books.google.co.jp/books?id=sHU ... 22&f=false
The oldest reference I found for the phrase "back in the day" is from the Bible, Psalm 78 (LXXVIII) where we find
. . . That they might set their hope in God, and not forget the works of God, but keep his commandments:
And might not be as their fathers, a stubborn and rebellious generation; a generation that set not their hears aright, and whose spirit was not steadfast with God.
The children of Ephraim, being armed, and carrying bows, turned back in the day of battle.
They kept not the covenant of God and refused to walk in his law . . .
One discussion I found said "[this] verse remains obscure, and many commentators suppose that it is an interpolation or that the text is in some way corrupt."
But in any case, the meaning of "back in the day" here is not the same as in the idiom in question. In the Bible, the action is "to turn back" and "in the day" is an adverbial establishing the time of that action.
The earliest use in the idiomatic sense being discussed here that I found using the Ngram Viewer is in "Drown" by Junot Diaz:
"Back in the day, before Cut's girl took over, he was Cut's gunboy but he was an irresponsible [expletive deleted], showed it around too much and talked amazing amounts of [expletive deleted]."
"Drown" is the debut short story collection by Diaz set in the 1980's and published by Riverhead Books in 1996. (First published in The New Yorker, Jan 29, 1996.) Diaz was born in the Dominican Republic and grew up in New Jersey, and the stories in the collection (also entitled "Drown") are semi-autobiographical. These facts suggest "back in the day" in the sense under discussion has its origin in the 1980's on the East Coast of the US.