Ok, the main keys to creature growth are:
Sleep. A creature grows quicker when sleeping, quicker still if he's in his pen and even more when at night.
Fat. A creature can not grow when at 0% fat since the energy needed for growth are taken from his fat reserves. 35% or more is recommended
Age. After the age of 18 a creature's growth rate slows down considerably.
All night maps have been used for a long time since it gets the creature to sleep in his pen at night for a maximum growth rate. Typically, two player maps were used. But the other player and creature did pose problems so you needed to watch what's going on in the map and couldn't leave it unattended. The Extreme Growth map is single player so you can leave you creature unattended for long periods. Provided he can take care of himself. People have gotten a full grown creature by this method in as little as 6 years. One of the down sides of this method is that your creature will always want to sleep in his pen at night. Which can be very annoying and is a hard habit to break him of.