Yup, totally has to be him. I never realized all this on the bio...
https://villains.fandom.com/wiki/Terry_Silver
"It was in Vietnam that Silver would meet one of the primary influences on his later life, Capt. John Kreese. Kreese, then a First Lieutenant, was the Commanding Officer of the infantry company which Silver was assigned to, and had already distinguished himself with heroic service in combat during the previous years of the war. Kreese was a specialist in long-range surveillance patrols and an expert in jungle warfare, and was invaluable to the young Silver as a mentor and if big brother figure. Silver credited Kreese with saving his life several times during harrowing night-time patrols in Vietnam's Central Highlands region, where the two came under enemy fire on countless occasions. Silver himself was awarded three Purple Heart medals over the course of his combat service from 1969 to 1972, and Kreese earned a Silver Star and was promoted to the rank of Captain.
In 1970, Kreese became the U.S. Army's Karate champion, at which point Silver requested that Kreese train him. Though he had no prior experience in Karate, Silver's exceptional athleticism and his physical stamina made him a natural for martial arts, and Silver began undertaking extensive Karate lessons from Kreese in between combat missions. Kreese, who had studied under Kim Sun-Yung of South Korea, instilled in Silver the creed of "Strike First, Strike Hard, No Mercy". The two continued their rigorous workouts and sparring matches throughout the remainder of the war, along with others in their infantry company so that more soldiers could learn the valuable hand-to-hand combat skills. It was this small but elite group of soldiers who became the very first "Cobra Kai" class, and all of them received a distinctive tattoo of a fist clutching a cobra, which was to become the symbol of their brotherhood"