Like most phrases, the exact origins of this saying are unknown, but there's an early printed use of it in The Syracuse Herald, an old newspaper from New York in 1918. There it reads:
"I have I shall rather enjoy the experience, though the stitlons are full of people trying to get out and the streets blocked with perambulators, bird cages and 'everything but the kitchen sink.' "
The fact that the idiom has quotations around it would imply it's already a known phrase at the time, so the phase is likely much older.
Additionally, there are claims that the phrase's origins are rooted in World War II, but seeing as how the quote in the newspaper came twenty-one years before, that doesn't seem to be the case. However, it's possible that the phrase became more commonly used around war times.
Reference: The newspaperarchive had a digitized form of this newspaper with the idiom in the quote above.
Note: The phrase origins, or history of particular idioms can be difficult to trace down, so finding the precise time a saying came into existance is no walk in the park. What you will usually find on this site are moments in history where an expression started to be used on a widely-known basis.
For instance, a lot of popular sayings can be spotted in old newspapers from several decades ago, but think about that for a second. If an idiom is being used in the media, it seems apparent that everybody already knows about it! What does that mean? Well, it means the origins of the phrase are probably much older.
On that note, what you'll, for the most part, find on this site are early usages of particular expressions, usually coming from aged books, plays, poems, or newspapers. It's meant to give you an estimate on how long certain phrases have been used for, but not necessarily where they originated from.
