Typically, it goes like this: I move my first warrior in his first move one tile away from the just founded capital. In turn 2 or 3, a barbarian scout appears on the opposite side of the capital and moves straight back to the barb camp which is four tiles away from my capital. In round 4 or 5 the first barbarian horseman appears, one turn later the next one and one turn later the next one. Neither my first warrior nor my first slinger have a chance against the horseman. And by the time I could have three or more warriors to be able to destroy that damn camp, the barbs can surround my city with horsemen. Then I mostly give up, because the AI has settled all around me and are many many techs ahead of me. I have given up hope that we will see another patch that fixes the barb problem. This will remain a major nuisance in the final version of Civilization 6.