Carter, a 6-foot-9 junior who redshirted last season after transferring from Seton Hall, was 10-of-17 shooting and blocked three shots. Terrell Brown made 5 of 6 from the field and scored 12 points for Seattle (2-1).
The Redhawks never trailed and took a nine-point lead into the break. Carter converted a 3-point play and hit a 3-pointer before Delante Jones and Matej Kavas hit back-to-back 3s to cap a 12-0 run to open the second half and Bryant trailed by at least 18 the rest of the way.
Byron Hawkins led the Bulldogs (0-2) with 19 points and Adam Grant added 12.
The Redhawks outscored Bryant 20-4 in second-chance points and 44-18 in the paint.