Always thought it was a bit weird how you instantly settle a pretty big city and your city can do everything just like that. I think you should start games with a normal Settler, a Builder, a Warrior and a Scout. When you settle you can put your worker in your city to have your city unlock Production or have him outside and build on tiles. Once you reach a certain population your cities will unlock Production. Your Warrior is the City's defense until you have built walls. I think there should also be wooden walls you build or research to help against barbarians or neighbor Civs. This would make the start more interesting and you would not rely so heavily on 'oh my god I have to settle on turn 1 or I'm done'.
Example:
You start the game. You scout about and see a really nice spot 5 tiles away from the start of your Settler, you go there and settle. There's also a nice bonus food tile you see. You pop a farm on it and take your Builder to your city. To get some whereabouts you take your Warrior to a nearby hill on alert. A new technology is researched, your Builder gives your City some Production but you spend 1 Builder points on a Granary to give it a Production boost. You spend the last one later on a nearby Luxury tile when Mining is complete.
Example:
You start the game. You scout about and see a really nice spot 5 tiles away from the start of your Settler, you go there and settle. There's also a nice bonus food tile you see. You pop a farm on it and take your Builder to your city. To get some whereabouts you take your Warrior to a nearby hill on alert. A new technology is researched, your Builder gives your City some Production but you spend 1 Builder points on a Granary to give it a Production boost. You spend the last one later on a nearby Luxury tile when Mining is complete.