And I thought it was impossible. Granted I was playing a Beginner game, but I'm still surprised I won on my third attempt. I achieved a diplomatic victory and I did it thanks to the advice I got here.
1. I put my 3 extra points into Research, Diplomacy, and Trade.
2. I went after alliances with a vengeance. I discovered that most of my AI's would accept an alliance for 5000+ bc!