Think of the techs in terms of what's needed to help people who don't have many resources survive... and that leads you straight to food, i.e. farming. It is possible though in the easy and normal mode, once you keep a careful check on your population, to get science first (and increase the speed at which you get farming). The only way to make the baby grow faster, other than 2x speed, would be to tamper with your system clock, which is definitely not advised, since that can lead to some pretty alarming results.

Think of the waiting as a way of increasing your own tech level in patience .. lol