I'm playing Brazil on Immortal right now. I've gotten Royal Library, Hanging Gardens and serveral other early wonders the AI tries to rush. On top of that I've built one of the largest armies on My continent and lead sience up until around renaissance. I still have a big cutural and tourism lead. How? Micro management. Place your citizens right. Check if new ways to place them is better every time you get a new one or build an improvement. Don't be afraid to focus produktion and lag behind on food to finish a wonder, you can compensate this by focusing on food or building a lot of food buildnings afterwards. Befriend city states that give good bonusens. Etc.