I wonder if war with two cities and axes/chariots is a good idea after all. In some cases maybe, but generally it seems slow way to expand. For me it takes always to 1500-1000 BC until the war is over. By then, you have 2 cities and enemy capital, and maybe 1-2 other enemy cities you don't really want to keep (badly placed). And other opponents have claimed best spots by then.
By expanding peacefully, you can have 5 well placed cities by 1000 BC. Sometimes it's possible to have 9-10 cities peacefully by 0 AD (standard maps, continents). With these, prince can be easily won (space, culture) without any offensive war. Science slider drops to 0% but it doesn't really matter as long as you don't go to strike. Libraries & scientists in 7-8 cities are enough to tech some crucial techs (code of laws, currency..) and when cottages develop, slider will go up. Imperialistic trait helps early expansion a lot (cheaper settlers)
And how? Build worker first (workboat if coastal+seafood), tech food techs and then bronze working, improve food resources, grow capital to 4, chop and whip a settler and second settler right away + warrior(s) to escort them. One settler goes to claim bronze/horses, other goes to claim some great city site near your opponent that is likely to go fast. In every city build monument (if not creative), granary, library, and after city reaches size 3-4, build and whip worker/settler. One city builds barracks and then nothing but troops (axes + some spears) that are sent to border cities. My tech line is usually food techs --> mining --> bronze --> mysticism (if not Creative) --> The Wheel --> Pottery --> Writing (for getting this crucial tech, I sometimes have to slow my expanding a bit).