First my first thought: "Wow, this is possible?"
However, when reading your post, a big issue is that you only have 4 cities in 1850AD. On normal speed this is something you should have by around 2000BC, or at least three cities by then. Important early game priorities is to build a worker (almost always do this as your first build in a city), improve the food, EXPAND. On Chieftain level you have looooooooooooooooots of time to do this before the AI does, so you must have been incredibly slow in this game.
Don't build all the buildings in the list, this is a typical mistake, but many of them aren't really worth building, especially early on.
This is a pretty common way to play the early game.
1. Build worker
2. (Simultaneously) Research the worker tech you need to improve food in your capital (unless you start with it). Typically Farming, Fishing or Animal Husbandry.
3. When the worker is out, improve your food
4. Build warriors until the capital hits size 3.
5. Start a settler.
6. Start another settler
7. Found two cities in good locations, that grabs food (Food is King) and maybe a strategic resource like Horses or Copper, if it's located nearby.
This should get you 3 cities by ~2000BC. Keep building some warriors and workers and settlers in this very early game. Unless you're going to rush (wage war on an AI very early), you need to grab land by expanding. Try to get at least 6 cities by 1AD, but aim for 10.
Points don't matter much btw. More important to develop your cities and empire, so just ignore the scoreboard for now, especially in the early game. It's largely population that matters, and since the AI will grow faster in the early game because you do smarter things, such as building workers and settlers (you can't grow while you do this), you will have fewer points. Doesn't matter. Civ4 is a marathon, not a sprint
