The United States and Soviet Union tried to outdo each other countless times during The Cold War, so it makes sense that a Russian version of Captain America would be created.
Regardless, once the Soviet Union collapsed, the original plans for Red Guardian fell through, leaving him to embark down a new life path.
That said, one can assume that unless David Harbour’s version of Red Guardian was somehow kept on ice for decades like Steve Rogers, he was created towards the end of the Cold War, unlike his comic book counterpart, who was active during World War II.