I've joked that my experience with very early offensive wars (pre-affinity 2) is 'like World War I', namely that the defensive capabilities of cities far outstrip the soldier/marine, especially when the AI starts with early armor units and usually a siege unit in the city itself.
Rushing for Affinity 2 and getting gunners does go significantly better. Usually a couple marines combined with 4 gunners can bring a city down before the city bombards my units to oblivion.
The first unique unit is a real game changer though, unless the AI just happens to invest in the early defensive buildings it's pretty easy to roll over multiple cities within a short time span. Even if they invest in the defensive buildings the gunners usually make short work of the defenses and the melee units can walk in.
I've tried to experiment with rushing cities earlier, but it almost always ends in me getting routed by the AI's high speed armor. My most successful early warfare efforts come when an AI declares war on me, attacks my frontier city that has a pair of gunners with it, loses most of its units, then I build momentum and counterattack.
Essentially this. With gunboats or better: cruisers you can do a lot of damage to cities that you cannot get with gunners or mobile artillery. Then bring one or two melee units for the kill as boats cannot capture a city.My most successful early game city attack only really works on coastal cities. But gunboats do a good job of damaging cities. Just bring 3-4, have them sitting out of range until you can get a land unit nearby. Move in all at once and bombard the city to ruins. Enjoy your walk in victory. Just remember that cities seem to prioritize ships for their counter attacks (probably due to them almost always one-shotting a ship, I haven't seen one live yet)
Getting gunboats isn't all that hard, if playing slavic, you could get if for free after getting one of the two starting techs next to it (if you get a lucky satellite).
Just have a stronger army and just wait for them to offer you the city for peace...don't even need to attack them. Of course they won't trade their Capitals. I really wish this would be fixed.
But yeah if you want to try and take it make sure to have a decent number of range units mix with melee.