This one require that you play maria of Austria which gives you the option to make a diplomatic marriage 5 turns after you have allied yourself with a city state. Usually cost somewhere in the range 1600-2000 gold.
The problem here is that most city states doesn't have 15 units and won't bother building that many at least not on the lower end of the difficulty scale, but don't worry it can be done even on settlers difficulty.
What you need is a good income so you can afford the marriage and the gifts the city state as an ally. beyond this you most likely also need to keep gifting them units, You can gift 1 unit every 3 turn. so you need to plan ahead, also keep in mind that they may disband the unit if they can't afford it, so don't forget to fill their treasury with gold. A good way of getting a supply of units to gift is by having other military city states produce them for you. So keep gifting them unit and gold and when you can count 15 units including workers and other none military. Save, then perform the marriage and this will be yours, if you counted wrong, reload the save and keep going and try again when you reached the right amount. Now you got a big army that you can use for a conquest victory.
since it takes some time to build up your country to manage this gold flow your bound to be mid-game before you can attempt this.