Can this actually be done?
There's two main ways to be better than everyone else at everything:
1) Quantitatively. If your empire is big enough, you will bury them.
2) Qualitatively. If you are either far enough ahead in science/culture or have a far superior economy, you will bury them.
Certainly even on emperor+ (notable because that's where the AI starts with a second settler) it's not hard to lead in diplomatic, science, culture, and score at the same time without resorting to conquering other civs. In fact, a big complaint about the new diplo victory is that even if you focus on it, you'll probably be in an easier position to win another victory before you win enough diplo votes.
A big part of this is making sure you both expand fast and have the research backbone to push ahead. Scotland is naturally suited here with boosts to science and production (amenities & great people.) +20% science & production from an ecstatic city is amazingly strong. The War of Liberation bonus to production is hard to rely on but also very nice to have - double production is nothing to sneeze at. You can declare a liberation war just to help rush districts/wonders if you need to.
If you don't mind a little warmongering then by far the best way to start a game is to take over one of your nearby neighbors if you have one. But if you prefer the challenge of peace, it's all about focusing science, culture, and production. Production is important so you can actually keep pace with your technology and most importantly, use those powerful cities to pivot into any projects you need. Projects help you win the world congress, secure great people, generate more science, and launch spaceships. Production = projects.
