Cold War
The world held its breath as each of the superpowers hovered their fingers of the proverbial Big Red Button. The Cold War was a time of unease, subterfuge, and geopolitical tension. With nuclear bombs being tested and the Berlin Wall being erected, wars were fought through proxies.
A Battlefield game set during the Cold War could utilize such elements as stealth, secret agents, and all manner of James Bond-like tropes. Given that it takes place shortly after World War 2, the weaponry and equipment used would become more modern as time went on.
The threat of nuclear warfare, and not knowing who to trust, could create excellent drama for a Battlefield game.