“Can’t Slam a Revolving Door” was a headline in The Architect and Engineer for October 1921. “The Hardest Job in the World—Slamming a revolving door” was published in a 1927 newspaper. “Add Things You Can’t Do—Slam a revolving door” was published in a 1929 newspaper. “Yesterday’s Tomorrow’s Simile: As futile as slamming a revolving door” was published in a 1946 newspaper.
 
“SOME SAY NOTHING IS IMPOSSIBLE! ever try slamming a revolving door?” was printed in a 1964 newspaper.  “Teenagers are the only people who can slam a revolving door”—the joke is that teenagers know everything—was published in the syndicated “It Happened Last Night” newspaper column of Earl Wilson (1907-1987) on June 30, 1960.
   
“Whoever said nothing is impossible never tried to slam a revolving door”—a popular form of the saying—was published in Earl Wilson’s newspaper column on April 16, 1978.
 
     
Wikipedia: Revolving door
A revolving door typically consists of three or four doors that hang on a central shaft and rotate around a vertical axis within a cylindrical enclosure. Revolving doors are energy efficient as they prevent drafts (via acting as an airlock), thus preventing increases in the heating or cooling required for the building. At the same time, revolving doors allow large numbers of people to pass in and out.
       
Google Books
October 1921, The Architect and Engineer, pg. 83:
Can’t Slam a Revolving Door
 
31 December 1927, Chicago (IL) Defender, “The Hardest Job in the World,” pt. 2, pg. 1, col. 6:
Slamming a revolving door.—M. Turner, Chicago.
 
25 February 1929, The Enquirer (Cincinnati, OH), “Along Life’s Detour” by Sam Hill, pg. 4, col. 7:
Add Things You Can’t Do.
Slam a revolving door.
     
6 October 1942, Brownsville (TX) Herald, “Good Afternoon!” by Jack Rutledge, pg. 4, col. 4:
Beal: “I’m a very determined man, and I can do anything I decide to do.”
Buddy: “Have you ever tried to slam a revolving door?”
 
29 December 1946, The Sunday Herald (Provo, UT), “Desk Chat, Editorial Column,” Editorial sec., pg. 4, col. 6:
Yesterday’s Tomorrow’s Simile:
As futile as slamming a revolving door.
     
30 June 1960, Winona (MN) Daily News, “It Happened Last Night” by Earl Wilson, pg. 4, col. 2:
EARL’S PEARLS: Teenagers are the only people who can slam a revolving door.
 
26 May 1964, Press Democrat (Santa Rosa, CA), pg. 16, col. 6 ad:
SOME SAY NOTHING IS IMPOSSIBLE!
ever try slamming a revolving door?
KVRE: POSER OF QUESTIONS AT 1460
     
16 April 1978, Daily Press (Newport News, VA), “It Happened Last Night” by Earl Wilson, pg. E10, col. 4:
Whoever said nothing is impossible never tried to slam a revolving door.

17 April 1978, Chicago (IL) Tribune, “Smile,” sec. 3, pg. 1, col. 5:
Whoever said nothing is impossible never tried to slam a revolving door.
—Quotable Quips
 
3 July 1981, Pittsburgh )PA) Post-Gazette, pg. 24, col. 4 ad:
Biz Whiz Bill Julin says the only thing that’s impossible is slamming a revolving door.
(Froggy’s, a saloon.—ed.)
 
31 May 1982, Trenton (NJ) Times, “A Tyger diet” by Frank Tyger, pg. C1, col. 4:
“Whoever said nothing is impossible,” claims George Dolan, “never tried to slam a revolving door.”
     
Google Books
14,000 Quips & Quotes:
For Speakers, Writers, Editors, Preachers, and Teachers
By E. C. McKenzie
Grand Rapids, MI: Baker Book House
1990, ©1980
Pg. 503:
Teen-agers are the only people who can slam a revolving door.
 
3 August 2001, Indianapolis (IN) Star, “Let It Out,” pg. E2:
The person who said that nothing is impossible never tried slamming a revolving door.
 
Twitter
Umar Nasir‏
@umarnasir
Whoever said nothing is impossible never tried slamming a revolving door.
7:34 PM - 29 Jun 2008
     
Google Books
The Sarcasm Handbook
By Lawrence Dorfman
New York, NY: Skyhorse Publishing
2017
Pg. ?:
“Whoever said nothing was impossible obviously never tried slamming a revolving door.” —UNKNOWN
 
Google Books
3000 Jokes, 2997 Laughs
By Mike Haskins
London, UK: Portico
2017
Pg. ?:
IMPOSSIBILITY. It is not true that nothing is impossible, as anyone who has ever tried to slam a revolving door will know.