Playing deity games without manipulation, I found the civ you play makes a difference due to its start bias. For example playing a grassland civ means you are just so vulnerable at the start without defensive cover.
I have had quite a few discussion with people that struggle between levels where one of the main issues appears to be how to defend properly, especially fortifying on rough and letting them hit you as opposed to hitting them.
Standing in front of the enemy before they have declared, slowing up their approach to your city weirdly works to buy you time as well.
Yeah, abusing AI pathing and combat proficiency is one of the things that work well on the "micro" scale of things.
The AI will often try to take down a fortified warrior on hills/forest if he's directly in the way of attacking a city, causing the AI to take terrible trades with his own warriors.
Depending on the extent of "terrible trades" for the AI, this is effectively letting the player get away with far fewer units (sometimes even winning the battle outright), or buying a lot of time for further defensive preparations.
Careful tactical retreat still has to be made occasionally though, as the player can't always afford to lose that particular warrior.
It can sometimes get rather hilarious when you have a chokepoint outside your borders though (for instance a single entry path between two mountains or two coast lines, where all tiles are covered by rough terrain).
In such occasions you can effectively just fortify and the AI warriors won't have enough movement points to "skip over" your warrior, causing a massive traffic jam, delaying (or outright stopping) the surprise war because their warriors can't get close enough for the AI to meet whatever their internal criteria is for a quick surprise attack on your city.
Even if they do decide to surprise war, there is often no way they can break a single fortified warrior on rough terrain, if that warrior only has one angle of attack (unless they happen to have archers on hills nearby, then it can get scarier) as you'll often just heal up at a rate fast enough compared to them bringing him down.
Either way though, there aren't always chokepoints like this to abuse, so in general a player needs to be aware of combat strength values (fortified, different types of terriain) and attack angles (I personally try to never let more than 2 warriors be able attack my 1, as 2 is the number where they might actually overpower you depending on combat strength values and RNG elements such as damage taken/dealt and whether or not any units have an upgrade/heal available.
Then there's also the importance of planning an escape route for that fortified position, unless it's absolutely vital that the warrior buys enough time with a last stand (preferably taking massively favourable trades) on that particular tile.
Abusing all these "little things" (as well as diplomacy, effective scouting etc.) is what usually sets up the early Deity game, and identifying and using these "little things" effectively comes with experience.
Fortunately though, these things flow rather natural once one gets used to them.
That being said though, your example with flat grassland starts absolutely applies, and in such positions it can get very dicey on Deity if an aggressive neighbour is nearby.