Leyrann
Deity
To be honest I am a little tired of reading such sentences, just because they are hardly realistic. Even if you do not move your starting warrior, you won't catch that scout who turns around the second he spots your capital. And I cannot clear a camp that is still in the fog of war. And because the human player is usually far behind in science in the early game, the barbarian units are more advanced than your own, and you need much time and many many units to clear a camp.
If you do not experience those things in your own games, you are one incredibly lucky person, congratulations. I wish you all the best and lots of fun!
It is indeed quite common for the player to be unable to clear a camp that spawns at game start before it scouts the player. However, that just means that if a scout finds your capital on turn 4, you switch to a slinger or warrior as soon as you finish your first scout. Assuming that's what you started with, of course. If you started monument or builder, you chose greed and should accept the risks associated with that.
You can find the camp simply by exploring the direction the barbarians came from.
In my experience (and this is on deity) camps do not start spawning more advanced units until at least turn 50; they can spawn horsemen earlier, yes, but those actually only have 20 combat strength, so if you simply put in the combat strength versus barbarians card your warriors can easily take care of them. The barbarian horse archers even more so, they don't deal all that much damage, but fall quite quickly if you attack them.
I am not a lucky person, I simply adapt my playstyle if needed so that I can deal with the barbarians. That's part of the game, and the design philosophy for Civ VI; you can't just close your eyes and cruise straight ahead, you have to adapt to the map and consider what the optimal strategy is with the hand you're given. And even then, I mean, bad games happen. Here's the screenshot I mentioned in the previous post:
View attachment 625538
Horsemen, horse archers, even a catapult - and I had already killed another catapult that came from the other direction, part of the army that attacked my capital and got it to zero health a few turns before this. (note how it's turn 63 and apart from the catapult it's all starting units)
How did I deal with it? By gearing my entire empire to fighting them, for the moment. I used the combat strength bonus against barbarians card, I selected oligarchy, and I even slotted in the Twilight Valor dark age policy, my first time ever (!) using a dark age policy. As you can see, I was also building quite a few military units (I lost several in my battles with the barbarians), and my warriors are at practically zero health because I was playing to the absolute limits.
But you know what? I got a great story to tell for it, and in the game itself, I recovered magnificently. Here's what the empire looks like only 107 turns after the above screenshot, now in the Industrial Era. Just look at the yields. And notice how I've caught up to most Deity AIs in terms of culture and science.
(oh and as it happens, I'm still dealing with barbs in the north, lmao)