OED1 (1897) has the following in its entry for the noun drink:
- U.S. humorous. A river or body of water.
Big drink : the Mississippi ; also, the Atlantic.
1857 Holland Bay Path xii. 137 So you'd better scull
your dug-out over the drink again, a i860 N. Y. Spirit of
Times (Bartlett Dict. Amer, s.v. Big), Off I sot, went
through Mississippi, crossed the big drink. 1873 Roots
(1888) 47 If you don't sit steady, we shall be spilt into the drink.
Thus, reference to a large body of water as a drink was established by the 1850's. But such usage as in the drink may be somewhat older than that. OED1's second main entry for the verb drink is like
Drink, Obs. Aphetic f. ADRINK, to drown.
c 1425 Seven Sag. ...
Hadde I than be dronken,
And in the salt flod sonkyn.
Cites for adrink are dated from 880 AD to 1300 AD. Aphesis refers to loss of the initial unstressed vowel of a word. Drink as the verb to drown was formed from the older word adrink, which if interpreted as an adverb could suggest in the drink.