Cold War: Approximately 1947 (due to U.S. President Harry Truman’s Truman Doctrine) to 1991 (Operation Desert Storm, collapse of Soviet Union).
The MTLB is a direct descendant of the PT-76 amphibious tank, as is the BTR-50, ASU-85, ZSU-23-4, and the 1S91 SURN-2K12 Kub antiaircraft missile system. However, all those other PT-76 relatives are rear engine/rear drive, the MTLB is mid-engine/front drive.
Photo dated March 1983, no other information.
The later MTLBu (also called M1976 by U.S./NATO) artillery command tank (mid-engine/front drive), 2S1 SP gun (front engine/front drive), and UR-77 (2S1 chassis) are based on a stretched MTLB chassis (with seven roadwheels instead of six, per side). The even later BMP-23 is based on the 2S1 chassis.
Photo I took one California National Guard drill weekend on NTC, California, in 1984. There were about a dozen MTLBs working with OpFor.
For some reason, NATO likes to add a dash between MT and LB, I have not found this to be the case with Russian sources. The MTLB comes from the Latinized Russian nomenclature; Mnogotselevoy Tyagach Legky Bronirovanny. In Russian Cyrillic it is Многоцелевой Тягач Легкий Бронированный, МТЛБ which is MTLB. In English it means Multipurpose Tractor Light Armored (MTLA). Light armored is for sure, I’ve checked out the MTLBs on Fort Irwin and the armor is so thin that I would not be surprised if 12.7mm (.50 cal) ball ammo could make Swiss cheese out of it.
Photo my father took of MTLB engineer vehicle at USAF air show in California, Summer 1986.
One of my Cold War era books on Soviet vehicles claims the MTLB was an armored version of the MTL (this claim is currently also being made by a internet ‘encyclopedia’). I haven’t found anything about an MTL, what I found is that the predecessor of the MTLB was the ATP, which has no relation to the PT-76 or MTLB. It’s not the first time NATO/U.S. was wrong about anything Soviet (COLD WAR BOATS: MOSKVA CLASS SUBMARINE HUNTERS, STOP CALLING THEM AIRCRAFT CARRIERS!).
During the Cold War, the U.S. Air Force managed to get their own Soviet MTLB. This one was seen on Bolling Air Force Base (now Joint Base Anacostia–Bolling), Washington DC. Photo by Don S. Montgomery, October 1986.
Photo by Don S. Montgomery, October 1986.
U.S. Army Opposition Forces (OpFor) MTLB on Fort Irwin National Training Center (NTC), California, 31MAR1988.
Anti-aircraft MTLB Strela from one of the last parades under the Soviet Union, November 1989.
An Iraqi MTLB damaged during the last battle of the Cold War; Desert Storm, March 1991. Photo by Staff Sergeant Dean W. Wagner.
U.S. Marines test drive a captured Iraqi MTLB during Desert Storm. Photo by Chief Warrant Officer-4 J.M. Rodriguez, February 1991.
Since the end of the unofficial Cold War, the MTLB has been continually modified by the many countries that still use it.
Several years after the end of the unofficial Cold War, the U.S. Marine Corps was using MTLBs in wargame Kernel Blitz ’97. U.S. Marine Corps photo by Lance Corporal Timothy J. Reynolds, 21JUN1997.
USMC MTLBs, June 1997. USMC photo by Gunnery Sergeant Daniel Mobley.
See more here: SOVIET ARMOR OF THE U.S. MARINE CORPS
A USA (U.S. Army) AH-64 Apache versus a USA MTLB armed with Strela antiaircraft missiles (NATO reporting name Gopher missiles) during an All Service Combat Identification Evaluation Test (ASCIET), on Fort Stewart, Georgia, March 1999.
The remains of another Iraqi MTLB, but this time it is 2003, and it is a ZSU-23-2 antiaircraft gun version. USMC photo by Lance Corporal Jennifer A. Krusen, 11APR2003.
An Iraqi MTLB, near that infamous prison, 11MAY2005. Notice the use of wide ‘snow’ tracks. U.S. Army photo by Specialist Ronald Shaw.
See more of Iraqi MTLB in IRAQI ARMOR, AFTER THE INVASION.
Ukrainian MTLB towing artillery into the disputed Donbas area, sometime in 2015.
Bulgarian MTLB mortar track. U.S. Marine Corps Photo by Corporal Justin T. Updegraff, 07JAN2016.
Bulgarian MTLB mortar track. U.S. Marine Corps Photo by Corporal Justin T. Updegraff, 07JAN2016.
See video of Bulgarian MTLB mortar tracks launching rounds in SOVIET ERA ARMOR USED BY NATO: BULGARIA, PLUS THE BULGARIAN BMP-23.
Russian Northern Fleet photo of artic MTLB (notice wider snow tracks), dated March 2016.
Pink camo MTLB mortar carrier, during artillery competition in Kazakhstan. Photo dated April 2017.
Convoy of artillery towing Ukrainian MTLB, sometime in 2018.
April 2018, Ukraine shows off its new MTLB ambulances to the public.
Finnish MTLB during wargame Arrow 18, on Pohjankangas Training Area near Kankaanpaa, Finland, 18MAY2018. U.S. Marine Corps photo by Sergeant Averi Coppa.
Polish MTLB, NATO’s Forward Presence Battle Group Latvia, during Operation Reassurance at Camp Ādaži, Latvia, 26JUL2018. Photo via Canadian Armed Forces.
Bulgarian Army MTLB during NATO Exercise Platinum Lion. North Carolina Army National Guard photo by Sergeant Jamar Marcel Pugh, 02AUG2018.
Video from Kazakhstan, 2021‘s International Army Games-Masters of Artillery Fire competition, showing the Russian team’s MTLB mortar carrier action:
September 2021, Russian Black Sea Fleet MTLB-9A35 launch their 9K35 Strela-10 (NATO reporting name SA-13 Gopher) missiles:
‘Z’ marked MTLB, Donbas AO, end of February 2022.
Russian MTLB in the Donbas Area of Operation, March 2022.
An abandoned/captured Ukrainian specialized MTLB, March 2022.
The 2S1 self propelled artillery gun is based on a stretched MTLB chassis:
2S1, FROM COLD WAR TO UKRAINIAN BORDER CRISIS!
NATO Bulgaria’s BMP-23 is based on the 2S1 chassis: 
BULGARIAN SOVIET ARMOR, PLUS THE BULGARIAN BMP-23
Cold War Vehicle I-D: 
BRDM-2, NOW BEING USED AS TAXIS?
IDAHO’S 1:1 SCALE FAKE NEWS RUSSIAN MTLB BASED 1S91 SURN TANK
RUSSIA INVADES FLORIDA with 2K12 KUB