If you're expanding, you're probably warring successfully. Make it a point to first war with a neighbor who can give you sufficient tech for peace. This is pretty easy in ancient times, if you put all of your eggs into the military basket. After that, pick your shots with the easiest targets: weak nearby civs, nearby cities isolated from the parent civ, any civ at all if you can make the right alliances. In the meantime, keep your research mostly at zero, and buy techs late at a discount. Lots of marketplaces and banks will make this easier. Target the Theory of Evolution wonder, as this will give you a shot in the arm that should carry you all the way to victory. Typically, this approach will result in an ebb and flow of tech. The first trough starts almost immediately, and lasts through that first war; the second one usually comes in the heart of the Middle Ages. If you fall too far behind at either point, you are probably lost, so it's critical not to panic at these times, and trust in the game's patterns.
