According to the author Tad Tuleja, in the book "The Good People: New Fairylore Essays":
citations in American archives mention elements of the custom dating from early in this century, the [..] genealogy, her development from folk belief to national custom and her contemporary social function all remais obscure
In an analysis of the myth genealogy, the author supplements:
Relying on Katharine Brigg's standard work, Rosemary Wells concludes that the dental sprite is America's only fairy - a creature "never referred to in European literature", and equally absent from Old World folklore
In the mentioned research of Rosemary Well, the estimated date of 1900 is likely the first appearance of mentions to the Tooth Fairy.
Also, quotations about the Tooth Fairy don't occur in researches on the bases of European mythological beings, discarding the possibility of this being its origin (and, therefore, first citation).
However, there are European quotations that resemble the fairy tale. The author Peter Narváez exemplifies the similarities between some European tales, and how they can be related, giving a clearer origin to the Tooth Fairy.
~ I used the same chapter structure as him, because I found the separation interesting.
The Tooth Coin as "Fairy Gold": "among the commonly cited attributes of fairies are their affluence and accompanying generosity; the pot at the end of the leprechaun's rainbow and the fairies's double payment of a debt to humans suggest a broad tradition of philantropic pixies. With this tradition in mind, Jacqueline Simpson once suggested that the Tooth Fairy exchange may derive from an Old British custom of rewarding industrious servent girls with "fairy" coins, left surreptitiously in their shoes as they slept".
The Tooth as a Propitiation or Self-Defense: "There are structural links between Tooth Fairy customs and folk pratices designed to foil such kidnappers. Since teeth have long simbolized imperishability, they function worldwide as talismans against evil. The tooth of a child, set near it as i sleeps, mitht be viwed, therefore, both as a form of preventive magic and more complexly, as a surrogate sacrifece - a pars pro toto offering for spirits who seek to snatch the child itself".
The Italian "Tooth Fairy" - Marantega: "The Venetian version of Befana (the Old One, la Vecchia, gaunt and toothless, a witch), called Marntega, displays generosity not only at Christmas season, but also when children lose teeth. A shed tooth is placed under the child's bed or under its pillow, and in the night Marantega exchanges it for a coin".
French Connection: "there are accounts of at least two Gallic tooth rituals that are roughly contemparary. In the first, from 1887, the child puts the tooth beneath its pillow and the Virgin Mary exchanges it for money or a toy. The second, from 1902, cites a 'good fairy' as the benevolent dental agent and the reward is candy, not money".
Chronology favors these French connections, although the genealogy is hazy. In contemporary French tooth exchanges, ir is a mouse, not a fairy, who takes the tooth; in a recent dictionary of French superstitions, the fairy agent is banished to uncivilized 'Anglo-Saxon' countries.
The Tooth Fairy and the "Tooth Mouse": shed teeth are offered to animals throughout Europe, with the commonest recipients being crows, other birds, and rodents. In the most widespread version of hole, behind furniture, or near the hearth or oven - and with a doggerel formula, asks the mouse to exchange it for a better one.
Disciples of Max Müller int the 1920s saw this ritual as a survival of ancient offerings to fire gods. Imaginatively linking the mouse to the sun, they attempted to explain at one stroke the three commonest methods of tooth disposal: whether the child hurled the tooth into the air, threw it into the fire, or offered it to a mouse, the common element was sun worship. In more recent, psychoanalytical interpretations, the mouse becomes a phallic symbol and the surrender ritual an act of compensation, both mirroring and dramatically resolvind the Oedipal fantasy.
Despite the similarities between the tales, as shown by the cited author, I believe that the safest is to say something between 1900.
In this book, The Good People: New Fairylore Essays (1991), there are more texts that deal with this theme and other fantastic tales. I recommend reading.
Editor NARVÁEZ, Péter. The Good People: New Fairylore Essays, Kentucky: The University Press Of Kentucky, 1991. 531 p.
ROGOW, Lee. The Tooth Fairy, Colliers, 1949.