Actually, this is exactly what I do. Take out the top dog and the AI does too.
In my most recent game around 1850 at Regent level, I (Egypt) was neck and neck with the Aztecs and gaining in military power. My score was *just* higher then theirs. They had their own continent and I was on a much larger one with the French and Russians. I was bigger so I could keep my lead and slowly gain.
France and I had never been to war and we had wiped out the Greeks, Romans, Germans, and English together. Our relationship was strained at times, but peaceful. The Russians on the other hand were different. We had been to war a couple times, but had eneasy peace the past 500 years or so. Her military was large, but mine was larger and more advanced. However, Russia had the tech lead and I couldn't catch up because those dang Aztecs kept declaring war on me and forcing me out of Democracy.
The Aztecs were going to try to keep me out of a Democracy to try to keep up and in the meantime the Russians would pass us both by in tech and launch a spaceship or nuke us both.
So I knew what to do. My military was already huge and I switched to Communist and ramped it up even more. I goaded the Russians and declared war (the French just sat back and watched). I also had 3 cities on the Aztecs continent with one airport. It took me about 30 years but I slowly wiped out all the 25+ size cities of the Russians down to under 6 and blasted through their defenders. You have GOT to have artililary support to do this. My 60+ artililary blasted all defenses along with my bombers and battleships. It was tough and I lost a city or two to them but I eventually have pushed them off the map down to one city on a 4 square island. I declared peace, getting all the tech they had in return so I am now caught up with my biggest rival gone. France outta be crapping their pants now because if they try to take me on I'll be able to shred 'em very easily.
As for the Aztecs, it was difficult, but I slowly took 6 cities until I got to a bottleneck of land. I was loaded up with 30+ tanks, 30+ Inf and Mech Inf and 20 + artililary along with a couple full carriers of fighters and bombers and they finally got scared and begged for peace.
And that is where I am now at 1960 or so. I plan to go back to a democracy to blast way ahead in tech, fortify my border with France (just in cast) and mass all my troops on the Aztecs continent in cast they get cute again and I will wipe them out.
So I should win by either space race or domination if the Aztecs decide to declare war again. They will not get a second chance.