A lot vs. Alot: 9 Grammatical Pitfalls
by 1914 (1903 as push), of uncertain origin; no evidence for the common derivation from an acronym of port outward, starboard home, supposedly the shipboard accommodations of wealthy British traveling to India on the P & O Lines (to keep their cabins out of the sun); as per OED, see objections outlined in G. Chowdharay-Best, "Mariner's Mirror," Jan. 1971; also see here. More likely from slang posh "a dandy" (1890), from thieves' slang meaning "money" (1830), originally "coin of small value, halfpenny," possibly from Romany posh "half" [Barnhart].
The cavalryman, far more than the infantryman, makes a point of wearing "posh" clothing on every possible occasion -- "posh" being a term used to designate superior clothing, or articles of attire other than those issued by and strictly conforming to the regulations. [E. Charles Vivian, "The British Army From Within," London, 1914]
[1903+; origin uncertain; perhaps fr the mid-1800s term posh, ''money,'' fr Romany pash, ''a half,'' referring to a half-penny; perhaps fr mid-1800s posh, ''a dandy,'' of unknown origin; perhaps fr early 1900s Cambridge University slang push or poosh, ''stylish''; perhaps a mispronunciation of polish; improbably an acronym for port out starboard home, said to be the formula for choosing the side of the ship with the most comfortable cabins on the steamer route from England to India or return; perhaps none of the above]