On the inside of the Driver side door, there is a label. Probably on the actual Vehicle frame rather than the door. On the top right corner there will be a 4 digit date stamp. Mine is 03/06.

This is the Month and year of the build. Remember though that the Shreveport Plant is turning out something like 23 or 24 H3's a day. You may find as I did some labels attached to some of the chasis components. These are Bar Coded labels that had the specific date of 03/27/06. This must have been my truck's born on date and was how the assembly plant monitored the completion of the vehicle in it's different stages on the line.
HTH