April 7, 2006 Officially.
There is always the POSSIBILITY, and regardless of speculation, NOBODY knows about this possibility YET (including WDW staff, due to the ride being so new) that there COULD be a "soft opening" at any time before that date.
http://www.disboards.com/showthread.php?t=1003899
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EXPEDITION EVEREST:
Grand opening: April 7, 2006
Designer: Walt Disney Imagineering, Vekoma
Mountain height: 199 feet
Ride height: 120 feet
Track length: 5,437 feet
Largest drop: 112 feet
Inversions: 0
Maximum speed: 50 mph
Height restriction: 44 inches
Capacity: Each train carries 34 passengers in 17 two-person rows
Restraint: Lap bar
Ride system: Roller coaster
Compared to other rides at WDW...
Splash Mountain Drop= 52.5 Feet
Splash Moutain Top Speed (the big drop)= 40mph
BTMRR Top Speed= 36mph
Space Moutain Top Speed= 28.7 MPH