To “hit the gym” means to go to the gym (to work out) There are many other “hit” sayings; “hit the sack” and “hit the hay” both mean to go to bed, and “hit the books” means to study.
   
“Hit the gym” was popular in the early 1900s with boxers.“Bob Laga, his manager, finds it difficult to keep the little fellow from indulging in too strenuous a time when he hits the gym” was printed in The Enquirer (Cincinnati, OH) on October 6, 1916. “Alger is hitting the gym daily and getting the kinks ironed out for his coming bout” was printed in The Arizona Republic (Phoenix, AZ) on January 14, 1922. “Upon his return he will hit the gym for a month to get in shape” was printed in the San Francisco (CA) Chronicle on June 17, 1924.
 
“I hit the gym, but I drove away because I don’t have car insurance” is a joke on the expression.
         
 
6 October 1916, The Enquirer (Cincinnati, OH), “Rivers Arrives,” pg. 8, col. 6: 
Bob Laga, his manager, finds it difficult to keep the little fellow from indulging in too strenuous a time when he hits the gym and it is only after considerable persuasion that Joe knocks off.
 
14 January 1922, The Arizona Republic (Phoenix, AZ), “Boxing,” pg. 8, col. 3:
Alger is hitting the gym daily and getting the kinks ironed out for his coming bout.
 
17 June 1924, San Francisco (CA) Chronicle, “Jimmy Dundee Is Planning to Stage Fight Come-Back” by Right Cross, pg. 2H, col. 2:
Upon his return he will hit the gym for a month to get in shape.
 
18 February 1926, Buffalo (NY) American, “Y.M.C.A. Notes,” pg. 4, col. 2:
Nineteen boys hit the Gym floor last Saturday at 9:30 and engaged in a spirited round of basketball.
   
11 April 1935, Great Falls (MT) Tribune, “Crowd Joins Rasslers in Gay Program,” pg. 10, col. 7:
“I’m going to hit the gym tomorrow and in four weeks I’ll lay a $200 side bet in any match with a legitimate resident of Montana for the state crown.”
 
17 October 1949, Milwaukee (WI) Sentinel, “Plant Reaches City, Works Three Rounds With Gomez,” pt. 2, pg. 4, col. 1:
Bobby Plant, who meets Alvin Jordan in the 10 round windup at the Riverview rink Monday night, arrived in town yesterday and wasted little time before hitting the gym.
 
1 August 1949, Stamford (CT) Advocate, “Union’s Film Of Strike Exposes ‘Wall Street’ Lie Of Communists” by Victor Riesel, pg. 4, col. 6:
... or George Meany, a portly, ex-fullback type who long since has been too busy to hit the gym regularly—go shake their hands.
 
15 January 1958, The Globe and Mail (Toronto, ON), “Mederos Getting Ready Quickly, Jack Allen Says,” pg. 17, col. 3:
Chuvalo, top contender for the vacant Canadian title, sparred over the weekend with Kurt Scheigle, formerly of Austria, then took Monday off before hitting the gym again yesterday.
 
Google Books 
The Gold’s Gym Book of Bodybuilding
By Ken Sprague and Bill Reynolds
Chicago, IL: Contemporary Books
1983  
Pg. 6:
As they grow older they don’t train as intensely as when they were competing, but they still hit the gym almost every day.
   
Google Books
January/February 1984, Cruise Travel, “The ship’s in shape…how’s yours?” by Marianne Gilbert, pg. 56:
Many start off their cruise with great intentions, hitting the gym and passing up desserts for the first couple of days.
 
OCLC WorldCat record 
Business - Health: Gym’ll fix it - If you’re a figure of fun after the festive period, one way to shed unwanted pounds is to hit the gym. But make sure you get a tailored service
Publisher: [London : Society of Incorporated Accountants and Auditors], 1938-
Edition/Format: Article Article : English
Publication: Accountancy. 129, no. 1302, (2002): 46
 
Urban Dictionary
Hit the gym
To head to the gym to work out.
Brandon: I’m really out of shape. I need to hit the gym soon.
#hit the weights#work out#lift#get in shape#pump iron
by awb475 June 29, 2010
   
OCLC WorldCat record
Hitting the Gym
Author: Stephen Easton
Edition/Format: Article Article : English
Publication: Australian Ageing Agenda, (Mar/Apr 2011): 38-39
Summary:
Gymnasiums are not yet among the standard amenities found in all residential aged care facilities, but a growing number of providers are going down that path. Stephen Easton looks at some who are leading the way and what could be holding others back.
 
Google Books
Title Gonna Hit the Gym: A 6x9 Inch Matte Softcover Notebook Journal with 120 Blank Lined Pages and a Gym Workout Cover Slogan
Author Getthread Journals
Edition illustrated
Publisher Amazon Digital Services LLC - Kdp Print Us, 2018
ISBN 1728859603, 9781728859606
Length 122 pages
 
Google Books
Title I Hit the Gym So I Won’t Have to Hit You: Fitness Motivation Workout Dot Grid Notebook, Journal Or Planner - Funny Weightlifting, Bodybuilding Athlete Gift Idea - Gym Diary - 110 Dotted Pages
Author Sports Notebooks
Publisher Independently Published, 2019
ISBN 1081788232, 9781081788230
Length 112 pages
 
Google Books
Title Hit The Gym? I Thought You Said Hit The Gin: Funny Gin Lover Daily Undated Planner, To-Do List, Appointment Schedule Notebook, Organizer
Author Magic Journal Publishing
Publisher Amazon Digital Services LLC - Kdp Print Us, 2019
ISBN 1075336392, 9781075336393
Length 102 pages