Played a game last night and did something that is fun but not always available.
A more powerful player started a fight. But I usually have a good navy early.
Went immediately to his Capital Provence and set up for a landing. as he was nearby.
Troops in my Capital wait one turn then attack the bigger players Capital. If you catch them with their troops spread out, you knee cap them immediately (take Capital).
I sit their laughing as the biggest player is now being picked apart by other players.
Not often, but when it works it is funny.

Rushing the capital is always a strategy as even if the computer player senses the attack, it cannot move all of its forces because they lack the transport capacity required. And it might be even the only thing to do if they are much more powerful than you.

That being said, when you conquer the capital like that, then all of the former GP's lands become available to be invaded by all computer players. They don't even need to declare a war (it is not possible anymore anyway). So there is a risk that GP's lands get shared across other GP's, although they did nothing to earn them.

Therefore, if possible, I first annex their colonies and then eat out their land and take the capital at last. But I see that this strategy is not always possible, especially in early game.