The earliest in the OED is from before 1636. The earliest I found is from the 1638 The Soules Preparation for Christ: a Treatise of Contrition by Thomas Hooker:
There are many that despight the spirit of grace, and stick not to say, I did sweare such a man out of the house, and I did drinke such a man under the table dead
Edit: This same book was also published in 1632 (EEBO [£]) and is the earliest I found of the verb drink in to drink someone under the table. The following aren't the same use of the verb, but are examples of someone being so drunk (or being made drunk) so as to be under the table.
A 1628 text by the rector Henry Burton warns on the dangers of drunkenness (in The seuen vials or a briefe and plaine exposition vpon the 15: and 16: chapters of the Revelation very pertinent and profitable for the Church of God in these last times, page 128, EEBO):
And aboue all, drunkennesse. For that strips a man of his garment, makes him naked, and men see his shame. Noah was once drunke, and he lay vncouered in his Tent, that his shame was seene. But now he is accounted no man, that will not drinke drunke, till he lie vnder the Table, like a dogg at his vomit, or wallow in the kennell, like a hogg in the mire.
Also from 1628, William Prynne wrote in Healthes: sicknesse. Or A compendious and briefe discourse; prouing, the drinking and pledging of healthes, to be sinfull, and vtterly vnlawfull vnto Christians by arguments, Scriptures, fathers, moderne diuines, Christian authors, historians, councels; imperiall lawes and constitutions; and by the voyce and verdict of prophane and heathen writers: wherein all those ordinary obiections, excuses, or pretences which are made to iustifie, extenuate, or excuse the drinking or pledging of healthes, are likewise cleared and answered (EEBO, page 17):
It is registred of the ancient Germans: that they sit drinking: and of the moderne Germans, that they sit Healthing night and day, till they haue laid one another dead drunke vnder the Table.
And on page 23:
Let it not be storied of vs, as it is of the Ancient and moderne Germans. (n) That they Carrouze, and Health, and Drinke so long, till they haue laid one another dead drunke vnder the Table, or caused one another to vomit vp their shame, and surfet: (a sinne to common in our swinish age) and a custome among Drunkards in (o) Saint Ambrose his dayes.
William Jemmat wrote in A spirituall trumpet exciting and preparing to the Christian warfare (1624, page 257, EEBO):
As for example: how many are there, who set themselues to make their brother drunken, and lay him vnder the table?