Okay, I'm still (slowly) playing through my first game. From my experience, plus what I'm reading here, I think a combination of factors are in play. However, the big one seems to be that the AI is generally as aggressive as you are. For the record, I'm on Prince, Standard size & speed, Continents.
I was also surprised when I ran into two civs early (Babylon and Egypt), but neither DoWed me. In fact, I got on Babylon's good side through some nice trades and my first trade route. Later ran into the Ottomans, and we four were the only full civs on this small continent (plus about half-a-dozen city-states).
Once I got some money flowing, Babylon suggested we attack Egypt. So I did.

Took his captial, razed another city, then took a rather generous peace offer. At this point, I also had a trade route to the Ottomans, and things seemed alright. However, he shortly afterwards had reverted to Neutral stance, and denounced me for trying to convert his cities, since Istanbul was applying craptons of pressure to my nearest city. Less than 10 turns later, he declares war.
This was the Medieval era. Wound up grinding to a stalemate, because terrain made it impossible for me to get close to Istanbul with his ranged defenders chewing me up. Wound up in an uneasy peace. Oh, and Babylon finished the job on Egypt, wiping them out entirely. I snagged one of the Egpyts two cities left, because I had just learned there was Coal next to it.

Babylon took the other.
In the meantime, I discovered that the other continent was pretty turbulent. Alliances kept shifting, based on the "We're glad you're friends with X/Don't get too cozy with X" statements. Monty wiped out one civ (I forget who) and went to war with Dido. That apparently wound up in a stalemate. By the Industrial era, Dido was at war with Russia, and finally took Moscow.
The commonality seems to be that AI civs who have good resources or good trade routes seem less likely to declare war
until they run out of expansion room
or you start inconveniencing them with faith/culture & your alliances (including Ideology). Then they get aggressive.
So, if you play traditional G&K openings, the AI has very little reason to be aggressive. Unless it just gets a bad start, it's more sensible to stay neutral or friendly while building up gold and Happiness. Actions by the player or other civs can push them into aggression, though.
I am curious if there's a correlation with map size/type. I know lots of folks who play Diety/Immortal also play Pangea maps. Wondering if that's part of the difference vs. lower difficulties or map type (less room to expand = more aggression sooner).