You cant 'speed up' production much early in the game... However some "optimization" do exist:
- Settling your capital on a Plains Hill gives you +1

. It can shave 3 turns from your first Worker, so 1 turn spent on moving the Settler up the hill is worth it...
- Beeing Expansive you get a bonus on

when building worker. So better Work a 3

tile, than 1

+2

(which is the same for non expansive leaders) - again can save you up to 3 turns on the first worker, assuming you have that one 3

tile (Forested Plains Hill). With Settlers same is true for Imperialsitic.
- Having a 3

tile and teching BW as first tech: Building Warrior first working the 3

tile. On turn 7 food bar has 21

(of 22 needed), so you switch to work a 1

+2

tile. Warrior will be done 3 turns later, you start worker, revolt to Slavery as soon as BW is done, and whip the Worker. This way on turn 16 you have a Warrior + Worker