Thanks for all the replies again!
My turns actually automatically progress. I have both fast turns and long turns running at the same time. The fast turns are for small things like warfare and the long turns are for bigger things like city and trade updates. This way I try to achieve a slightly more real-time experience for warfare. That's why in this game I think some early things to with the armies like claiming area's and skirmishes would work well.
What if you made the early portion of the game a nomadic phase?
Don't tie the civilizations to cities initially but give them nomadic units that explore, harvest resources, and make contact with other civilizations. They can establish small settlements near resources and once you acquire enough tech and resources then you can establish your first city. Building a city should be a a major undertaking. It could be done in stages by upgrading settlements or all at once if you find an ideal location.
That's one thing I always found lacking in CIV. You have to build a city on your first turn otherwise it counts against you and the map seed in the latest one ensures you have a mix of resources near your starting point. But there is no initial exploration or growth from nomadic people into an empire. Building your first city should be an major accomplishment it should be placed in a strategic location either at a cross road of trade routes, or with access to large amounts of valuable resources and of course it should be on a river. Since almost all major cities are either on the coast or on a river.
Nice idea but I fear this would be too drastic of a change at this point.