One of the things I've observed about many games is that the overly aggresive player at the table usually loses, along with whoever is unfortunate enough to be seated next to them, since they spend so much time fighting others can get objectives. That being said, it's nearly impossible (there are exceptions, such as if you're playing xxcha or hacan) to win a game without getting into a fight with your neighbors, usually over territory (no, that's MY tech bonus planet) or mecatol rex.
So, from your experiences, what is the right time to get aggresive? Some say it's around the time stage II objectives come out since many require all out war in order to get them, but I've seen players get serious prior to that. I'm not talking about little skirmishes, where two people go for the same random system and one gets it, and then it stays that way for most of the game because the loser has more important things to deal with. I'm talking about going for MR and keeping it, or trying to beat someone into submission so that they're not a threat anymore.