Kostiuk attended Hamtramck High School from 1934–1937, where he made All-City in 1935 and 1936, Detroit Tech from 1937-1940 on a footballscholarship. In 1939, he earned a position on the Little All-American Team. The players on this elite team were chosen from Class B colleges throughout the country. He left Detroit Tech in 1941 to play for the Cleveland Rams. In 1942 he entered the United States Army and continued his football career there, making the Armed Forces All-Star team in 1943.