I've never gotten a sense of being a monghilsbin or a ghbegis either.

Seriously though, I feel this is the problem for most civs in this game. I restart often to get a start that makes me 'feel' like it belongs to my civ. Civ VI felt more like that in my opinion, where I got bonuses from hills, or trees, and was put there.
I see people quoting how they like combinations or post screenshots of yields and how they got there, but I just don't get the sense of any "this is what I'll be doing that makes my empire greater than the others". It's really hard to put a finger on for me.
Civ has had a problem with starting positions being in any way relevant to the Civ or its attributes and bonuses since at least Civ IV, and Civ VII is no better. I still remember restarting Civ VI or Civ V 10 times or more trying to get a coastal start for England or Norway/Vikings or a desert start for Morocco or Nubia.
Civ VII's version seems to be a Tundra/Taiga start for everybody except Maya or Maurya or Trung Trac. With anybody else I get a Tundra/Taiga start well over half the time and if I restart more than twice I will get a High Latitude start every single time.
And, as you say, the sunny hills of Rome just don't feel right covered with snow and evergreen taiga forests, no matter what kind of bonuses the game gives me for that terrain.
I think part of, if not the fundamental, problem is the terrain bonuses, which are artificial and apparently designed to make every biome both useful and distinct: as if the difference between a forest of conifers and a forest of hardwood deciduous trees was Game Changing for any Civ.
Also, the fact that almost no Civ (so far) can fundamentally change the bonuses they receive from any biome in the game, no matter how long they live there, unless that change is built in to their Game Description. No matter how clever the Mississippians are, they cannot get anything out of a forest that the Mongols or Persians can't, despite those two groups being almost totally unfamiliar with a forest environment in reality (and the fact that the North American woodland natives that include both the Mississippians and Shawnee had well-established methods of cultivating and managing the forest to get the most out of it, which resulted in a very artificial environment that Europeans didn't even recognize as artificial!)
I'e suggested before, given the Civ games' utter inability to handle the starting biome problem, that I would prefer that the starting sequence was changed to reflect the fact that Some Civs Belong In Some Environments. That is, the Start Sequence should be:
Pick your map type and characteristics (and let's include options like an overall dry, or wet, or cold, or hot map)
Show the start position on that map.
Pick your Civ from a list of Civs that roughly match that biome - or not, as you chose. But if you want to play Mongols on a dry, cold plain that should be up to you, not the whims of map generation that are gratingly random.