There are no warmonger penalties in the Ancient era (and only light ones in Classical), so the AI is more aggressive early on and then settles down a bit (in most cases). However, in my experience (admittedly limited, as I haven't played beyond Medieval yet), if they perceive you as weak, they will be relentless about utilizing the opportunity. You can't ignore military in Civ VI, even if you go the peaceful builder / diplomatic route.
Not saying that the AI isn't a little bonkers, but there is *some* method to their madness. Now the touchiness about close borders needs to be taken down a notch (or ten), and the agenda system is a bit messed up, but I'm sure they'll address these issues in a patch a while down the road. I'd advise some patience, or simply mod the game's default aggression values from the files yourself (I'm pretty sure it can be done with a simple text editor, with a little digging).