Green’s Dictionary of Slang

sosh n.¹

(US) a state of drunkenness.

1899

W.J. Kountz Billy Baxter’s Letters 43: He saw Johnny Black a few minutes ago in a down-town place with a beautiful sosh on, and that he was eating his checks because he was broke.

In phrases

have a sosh on (v.)

to be drunk.

1908

Sporting Times 11 July 1/4: He had a beautiful sosh on, but was bravely bellying up to the bar in a British Columbian town.