The “waiter’s-thumb-in-the-soup” joke dates to at least 1883. The central joke is that hot soup can burn the waiter’s thumb (while the customer is more concerned about the cleanliness of the establishment).
 
One joke has the customer tell the waiter that the waiter’s thumb is in the soup. The waiter thanks the customer for looking out for him, but assures the customer that “the soup’s not that hot.”
 
Another joke has the customer demanding hot soup. The waiter is horrified: “What do you want me to do? Burn my thumb?”
 
   
21 June 1883, Weekly Hawk Eye and Telegraph (Brulington, IA), pg. 6, col. 4:
“This soup, waiter, is cold. Can’t you bring me some warm soup?” “Why, sah, you mus’ be mistakin’, sah. Dat soup was so hot dat it took all the skin off my thumb when I fetched it in, sah.” The stranger concludes that he will forego the soup and take a walk.—Yonkers Gazette.
 
22 June 1884, Washington (DC) Post:
“Waiter, I saw your thumb in this soup as you were bringing it to me!”  “Oh, you’re kind, I’m sure, sir, but it’s of no consequence.  It wasn’t hot enough to hurt much, sir.”
 
Papers Past
13 September 1884, Otago (New Zealand) Witness, pg. 28, col. 4:
“Waiter, I saw your thumb in this soup as you were bringing it to me!”  “Oh, sir, you’re kind, I’m sure, sir, but it’s of no consequence.  It wasn’t hot enough to hurt much, sir.”—Old Lake.
 
Papers Past
26 June 1891, North Otago (New Zealand) Times, pg. 4, col. 1:
On the Bowery, — Customer: “Why look here, waiter; you’ve got your thumb in my soup!” Waiter: “Ob, don’t mmdj ‘taint hot.” — Judge.
   
17 May 1902, Grand Rapids (MI) Tribune, pg. 4, col. 3:
In a University Dining Hall.
Student—Be careful, waiter. You have your thumb in my soup.
Waiter—Never mind; It isn’t hot.
—Judge.
 
9 July 1934, Edwardsville (IL) Intelligencer, pg. 2, col. 4:
Guest—See here, waiter, you’ve got your thumb in my soup.
Waiter—Oh, that’s all right, sir, the soup’s not hot.
   
Google Books
Thesaurus of Humor
By Mildred Meiers and Jack Knapp
New York, NY: Crown Publishers
1940
Pg. 476:
4778
Diner: Waiter, this soup is cold. Bring me some that’s hot.
Waiter: What do you want me to do? Burn my thumb?
 
21 November 1940, Nebraska State Journal (Lincoln, NE), “Mutt and Jeff” comic strip, pg. 4:
Diner: WAITER, YOU HAVE YOUR THUMB IN MY SOUP!
Jeff: OH, THAT’S O.K., SIR! THE SOUP’S NOT HOT!
     
15 January 1957, Los Angeles (CA) Times, “In Low Geyer’ by Jack Geyer, pg. B5:
And you complain about the soup being cold:
The waiter snaps, “Whatcha want me to do, burn my thumb?”
     
Google Books
The New Speaker’s Treasury of Wit and Wisdom
By Herbert V Prochnow
New York, NY: Harper
1958
Pg. 91:
COMPLAINT
Diner: “Waiter, this soup is cold. Bring me some that’s hot.”
Waiter: “What do you want me to do— burn my thumb?”
 
Google Books
Steve Allen’s Private Joke File
By Steve Allen
New York, NY: Three Rivers Press
2000
Pg. 221:
DINER: Waiter, your thumb us un the soup!
WAITER: Oh, it’s all right, ;ady, it isn’t that hot.