So, it's the height of the Cold War in the mid-1980s, when the USA and Soviet Union were at the closest to nuclear war they'd ever get after the Cuban Missile Crisis (in the real world, things were so tense that just two years earlier the two sides came seconds away from launching their nuclear arsenals). A stricken U.S. communications ship drifts into hostile waters, prompting the aircraft carrier USS Enterprise to launch its Tom Cruise, which engages and destroys four MiGs, forcing the remaining two MiGs to flee.
It's portrayed as a consequence-free victory in the movie, but by engaging in aggressive military actions without a formal declaration of war, the pilots of Top Gun forced the U.S. into a de facto state of war with North Korea (or whatever nation commanded those MiGs). Thanks to them, it's only a matter of time before said unnamed country addresses the United Nations about how the U.S. violated Article V of U.N. General Assembly Resolution 3314 by destroying some of their finest aircraft and killing some of their top pilots.
"Hell yeah, we did."
So the U.S. is either at war with the Soviet Union after engaging MiGs from their Pacific squadron, or Tom Cruise just kicked off a second Korean War with a North Korea so formidable they are now operating outside of the Pacific. Either way, the rest of the world has just been subjected to World War III, and it's pretty tough to play volleyball in a fallout suit.