That might be a decent method, though you'd need to work out the best stage for that to kick in. You couldn't have it happen too early, or too late.
I agree. That is why I mentioned "at least score of 500". The idea is that it would only kick in once you reach a certain score threshold. Sorry. I should have been more explicit. This way it would not start too early. For example, you could get a big early start where say on turn 50, you are already 2x bigger than the #2 but you don't want the mechanic to kick in on turn 50. It would only kick in on say turn 200 which would give everyone a decent chance to get ahead or catch up. Or you could set the threshold at say score 500 like in my example. This way it would only trigger once civs reach a certain score level. If you set the threshold right, I think you can have it kick in at the right time, not too early but too late either.
That is one of the issues, how will the AI understand that you are close to getting a victory? In some previous victory types I guess it is kind of obvious, if you are so far along building spaceship parts, that might be a point where the AI decides they need to team up and get you. The question is whether the AI is prepared to even compete against you to prevent you winning, and whether it is able to do so.
You could give players a warning when the game is close to the snowball threshold. Using my example above, if the snowball mechanic only kicks in on turn 200, if the #1 civ has a score 2x bigger than the #2 and it is turn 150, you would get a warning that the #1 civ is only 50 turns away from hitting the snowball threshold. Maybe have another warning at 20 and then 10 turns from the snowballing threshold.
Is the only way to compete just by building a military and smashing you down?
In most civ games, yes unfortunately. That is because there are no effective mechanics to catch up other than military. Or put differently, I think military conquest is often too strong in 4X games. Taking cities away from the other civ has a double effect of reducing their power but also increasing your power. So conquering the snowballing civ is the most direct way to stop them. So even if there are non-military solutions, the military solution is often the most effective.
The game needs to give civs more non-military tools to fight. Players need more peaceful ways to hurt other civs.
This is why espionage needs to be a bigger deal. I think espionage is the perfect mechanic to stop snowballing civs without using military force. You could use espionage to sabotage the snowballing civ, to slow down production or science, slow down a wonder construction. You could even sabotage the spaceship construction to slow down a science victory. You could also use espionage to steal tech to help catch up in science or steal great works to catch up in culture. Espionage also makes cold wars more interesting since two strong civs could resort to an espionage war as a way of hurting each other without escalating to military force. This would be especially true in the Modern Age when both sides have nukes and don't want to risk an all out war. This would be historically accurate too.
Economic warfare should also be a thing. You should be able to impose sanctions to hurt the civ economically. Imagine if civs joined together to all impose economic sanctions on the #1 civ. That could work without needing the AI to be good at waging war.